Semidirekte Produkte endlicher Gruppenschemata: Gabriel-Köcher und Auslander-Reiten-Komponenten

Let G be a connected algebraic group over an algebraically closed field k. If char(k)=0, then there is a strong correspondence between representations of G and those of its Lie algebra \g. This changes dramatically in the situation char(k)=p>0 of positive characteristic. In this case, it turned out to be useful to approximate G by the ascending sequence (G_r)_{r\geq 1} consisting of its so-called Frobenius kernels. Each G_r is an infinitesimal group scheme, it is not uniquely determined by its group of k-rational points anymore; in fact, the latter are trivial. Its representation theory is equivalent to that of the dual Hopf algebra kG_r:=k[G_r]^* of its finite-dimensional coordinate ring k[G_r]. The Hopf algebra kG_1 is isomorphic to the restricted universal enveloping algebra \U_0(\g) of \g which shows that the representation theory of G_1 is equivalent to that of \g as a restricted Lie algebra. The representation theory of \g itself can be approximated by studying the family \{\Uchi(\g):\chi\in\g^*\} of its reduced enveloping algebras. Many results are known in case of reductive groups. In general, every group G is an extension of a reductive group H by a unipotent group U. If U is non-trivial, then the 'next best' case is that this extension splits, which in turn leads to a semidirect product G=U\rtimes H. Since the functor G\mapsto G_r is left exact, the rth Frobenius kernel of G is then the semidirect product U_r\rtimes H_r of the Frobenius kernels of U and H. It is exactly this point of view on which this thesis is build upon. Simple G_r-modules correspond to simple H_r-modules via the inflation functor mod(H_r)\to mod(G_r) defined by pullback along the projection G_r\to H_r and the principal indecomposable G_r-modules are induced by principal indecomposable H_r-modules. We will also establish a formula for the Gabriel quiver of the Hopf algebra kG_r and analyze the behaviour of the inflation functor in terms of Auslander-Reiten sequences. Furthermore, we will show that the stable Auslander-Reiten quiver of kG_r does not admit components of Euclidean type. We will formulate these results more general for finite group schemes and certain reduced enveloping algebras of restricted Lie algebras. As a major example, we will consider the Schrödinger group S:=H\rtimes SL(2), the semidirect product of the reductive group SL(2) with the Heisenberg group H\subseteq \SL(3), along with its quotient \Sbar\cong \G_a^2\rtimes SL(2) by the center. The group S has already been considered over the field of complex numbers and is related to physics. We will show that the Gabriel quivers of the Hopf algebras of the Frobenius kernels of S and \Sbar are all connected and take a closer look at reduced enveloping algebras U_\chi(\sbar) of the restricted Lie algebra \sbar=\Lie(\Sbar)

Search for high-mass exclusive diphoton production with tagged protons in proton-proton collisions at s= \sqrt{s} = 13 TeV

A search is presented for high-mass exclusive diphoton production via photon-photon fusion in proton-proton collisions at $\sqrt{s} =$ 13 TeV in events where both protons survive the interaction. The analysis utilizes data corresponding to an integrated luminosity of 103 fb$^{-1}$ collected in 2016--2018 with the central CMS detector and the CMS and TOTEM precision proton spectrometer (PPS). Events that have two photons with high transverse momenta ($p_{\mathrm{T}}^{\gamma} >$ 100 GeV), back-to-back in azimuth, and with a large diphoton invariant mass ($m_{\gamma\gamma} >$ 350 GeV) are selected. To remove the dominant inclusive diphoton backgrounds, the kinematic properties of the protons detected in PPS are required to match those of the central diphoton system. Only events having opposite-side forward protons detected with a fractional momentum loss between 0.035 and 0.15 (0.18) for the detectors on the negative (positive) side of CMS are considered. One exclusive diphoton candidate is observed for an expected background of 1.1 events. Limits at 95% confidence level are derived for the four-photon anomalous coupling parameters $|\zeta_1|$ 100 GeV), back-to-back in azimuth, and with a large diphoton invariant mass ($m_{\gamma\gamma} \gt$ 350 GeV) are selected. To remove the dominant inclusive diphoton backgrounds, the kinematic properties of the protons detected in PPS are required to match those of the central diphoton system. Only events having opposite-side forward protons detected with a fractional momentum loss between 0.035 and 0.15 (0.18) for the detectors on the negative (positive) side of CMS are considered. One exclusive diphoton candidate is observed for an expected background of 1.1 events. Limits at 95% confidence level are derived for the four-photon anomalous coupling parameters $\lvert\zeta_1\rvert \lt$ 0.073 TeV$^{-4}$ and $\lvert\zeta_2\rvert \lt$ 0.15 TeV$^{-4}$, using an effective field theory. Additionally, upper limits are placed on the production of axion-like particles with coupling strength to photons $f^{-1}$ that varies from 0.03 TeV$^{-1}$ to 1 TeV$^{-1}$ over the mass range from 500 to 2000 GeV

Search for central exclusive production of top quark pairs in proton-proton collisions at s\sqrt{s} = 13 TeV with tagged protons

International audienceA search for the central exclusive production of top quark-antiquark pairs ($\mathrm{t\bar{t}}$) is performed for the first time using proton-tagged events in proton-proton collisions at the LHC at a centre-of-mass energy of 13 TeV. The data correspond to an integrated luminosity of 29.4 fb$^{-1}$. The $\mathrm{t\bar{t}}$ decay products are reconstructed using the central CMS detector, while forward protons are measured in the CMS-TOTEM precision proton spectrometer. An observed (expected) upper bound on the production cross section of 0.59 (1.14) pb is set at 95% confidence level, for collisions of protons with fractional momentum losses between 2 and 20%

Search for high-mass exclusive diphoton production with tagged protons in proton-proton collisions at s\sqrt{s} = 13 TeV

International audienceA search is presented for high-mass exclusive diphoton production via photon-photon fusion in proton-proton collisions at $\sqrt{s}$ = 13 TeV in events where both protons survive the interaction. The analysis utilizes data corresponding to an integrated luminosity of 103 fb$^{-1}$ collected in 2016-2018 with the central CMS detector and the CMS and TOTEM precision proton spectrometer (PPS). Events that have two photons with high transverse momenta ($p_\mathrm{T}^\gamma >$ 100 GeV), back-to-back in azimuth, and with a large diphoton invariant mass ($m_{\gamma\gamma} \gt$ 350 GeV) are selected. To remove the dominant inclusive diphoton backgrounds, the kinematic properties of the protons detected in PPS are required to match those of the central diphoton system. Only events having opposite-side forward protons detected with a fractional momentum loss between 0.035 and 0.15 (0.18) for the detectors on the negative (positive) side of CMS are considered. One exclusive diphoton candidate is observed for an expected background of 1.1 events. Limits at 95% confidence level are derived for the four-photon anomalous coupling parameters $\lvert\zeta_1\rvert \lt$ 0.073 TeV$^{-4}$ and $\lvert\zeta_2\rvert \lt$ 0.15 TeV$^{-4}$, using an effective field theory. Additionally, upper limits are placed on the production of axion-like particles with coupling strength to photons $f^{-1}$ that varies from 0.03 TeV$^{-1}$ to 1 TeV$^{-1}$ over the mass range from 500 to 2000 GeV

Search for high-mass exclusive diphoton production with tagged protons in proton-proton collisions at s\sqrt{s} = 13 TeV

International audienceA search is presented for high-mass exclusive diphoton production via photon-photon fusion in proton-proton collisions at $\sqrt{s}$ = 13 TeV in events where both protons survive the interaction. The analysis utilizes data corresponding to an integrated luminosity of 103 fb$^{-1}$ collected in 2016-2018 with the central CMS detector and the CMS and TOTEM precision proton spectrometer (PPS). Events that have two photons with high transverse momenta ($p_\mathrm{T}^\gamma >$ 100 GeV), back-to-back in azimuth, and with a large diphoton invariant mass ($m_{\gamma\gamma} \gt$ 350 GeV) are selected. To remove the dominant inclusive diphoton backgrounds, the kinematic properties of the protons detected in PPS are required to match those of the central diphoton system. Only events having opposite-side forward protons detected with a fractional momentum loss between 0.035 and 0.15 (0.18) for the detectors on the negative (positive) side of CMS are considered. One exclusive diphoton candidate is observed for an expected background of 1.1 events. Limits at 95% confidence level are derived for the four-photon anomalous coupling parameters $\lvert\zeta_1\rvert \lt$ 0.073 TeV$^{-4}$ and $\lvert\zeta_2\rvert \lt$ 0.15 TeV$^{-4}$, using an effective field theory. Additionally, upper limits are placed on the production of axion-like particles with coupling strength to photons $f^{-1}$ that varies from 0.03 TeV$^{-1}$ to 1 TeV$^{-1}$ over the mass range from 500 to 2000 GeV

Search for central exclusive production of top quark pairs in proton-proton collisions at s\sqrt{s} = 13 TeV with tagged protons

International audienceA search for the central exclusive production of top quark-antiquark pairs ($\mathrm{t\bar{t}}$) is performed for the first time using proton-tagged events in proton-proton collisions at the LHC at a centre-of-mass energy of 13 TeV. The data correspond to an integrated luminosity of 29.4 fb$^{-1}$. The $\mathrm{t\bar{t}}$ decay products are reconstructed using the central CMS detector, while forward protons are measured in the CMS-TOTEM precision proton spectrometer. An observed (expected) upper bound on the production cross section of 0.59 (1.14) pb is set at 95% confidence level, for collisions of protons with fractional momentum losses between 2 and 20%

Search for high-mass exclusive diphoton production with tagged protons in proton-proton collisions at s\sqrt{s} = 13 TeV

International audienceA search is presented for high-mass exclusive diphoton production via photon-photon fusion in proton-proton collisions at $\sqrt{s}$ = 13 TeV in events where both protons survive the interaction. The analysis utilizes data corresponding to an integrated luminosity of 103 fb$^{-1}$ collected in 2016-2018 with the central CMS detector and the CMS and TOTEM precision proton spectrometer (PPS). Events that have two photons with high transverse momenta ($p_\mathrm{T}^\gamma >$ 100 GeV), back-to-back in azimuth, and with a large diphoton invariant mass ($m_{\gamma\gamma} \gt$ 350 GeV) are selected. To remove the dominant inclusive diphoton backgrounds, the kinematic properties of the protons detected in PPS are required to match those of the central diphoton system. Only events having opposite-side forward protons detected with a fractional momentum loss between 0.035 and 0.15 (0.18) for the detectors on the negative (positive) side of CMS are considered. One exclusive diphoton candidate is observed for an expected background of 1.1 events. Limits at 95% confidence level are derived for the four-photon anomalous coupling parameters $\lvert\zeta_1\rvert \lt$ 0.073 TeV$^{-4}$ and $\lvert\zeta_2\rvert \lt$ 0.15 TeV$^{-4}$, using an effective field theory. Additionally, upper limits are placed on the production of axion-like particles with coupling strength to photons $f^{-1}$ that varies from 0.03 TeV$^{-1}$ to 1 TeV$^{-1}$ over the mass range from 500 to 2000 GeV

Search for central exclusive production of top quark pairs in proton-proton collisions at s\sqrt{s} = 13 TeV with tagged protons

International audienceA search for the central exclusive production of top quark-antiquark pairs ($\mathrm{t\bar{t}}$) is performed for the first time using proton-tagged events in proton-proton collisions at the LHC at a centre-of-mass energy of 13 TeV. The data correspond to an integrated luminosity of 29.4 fb$^{-1}$. The $\mathrm{t\bar{t}}$ decay products are reconstructed using the central CMS detector, while forward protons are measured in the CMS-TOTEM precision proton spectrometer. An observed (expected) upper bound on the production cross section of 0.59 (1.14) pb is set at 95% confidence level, for collisions of protons with fractional momentum losses between 2 and 20%

Nonresonant central exclusive production of charged-hadron pairs in proton-proton collisions at s\sqrt{s} = 13 TeV

International audienceThe central exclusive production of charged-hadron pairs in pp collisions at a centre-of-mass energy of 13\TeV is examined, based on data collected in a special high-$\beta^*$ run of the LHC. The nonresonant continuum processes are studied with the invariant mass of the centrally produced two-pion system in the resonance-free region, $m_{\pi^+\pi^-}$$\lt$ 0.7 GeV or $m_{\pi^+\pi^-}$$\gt$ 1.8 GeV. Differential cross sections as functions of the azimuthal angle between the surviving protons, squared exchanged four-momenta, and $m_{\pi^+\pi^-}$ are measured in a wide region of scattered proton transverse momenta, between 0.2 and 0.8 GeV, and for pion rapidities $\lvert y\rvert$$\lt$ 2. A rich structure of interactions related to double-pomeron exchange is observed. A parabolic minimum in the distribution of the two-proton azimuthal angle is observed for the first time. It can be interpreted as an effect of additional pomeron exchanges between the protons from the interference between the bare and the rescattered amplitudes. After model tuning, various physical quantities are determined that are related to the pomeron cross section, proton-pomeron and meson-pomeron form factors, pomeron trajectory and intercept, and coefficients of diffractive eigenstates of the proton

Search for central exclusive production of top quark pairs in proton-proton collisions at s= \sqrt{s} = 13 TeV with tagged protons

A search for the central exclusive production of top quark-antiquark pairs ($\mathrm{t} \bar{\mathrm{t}}$) is performed for the first time using proton-tagged events in proton-proton collisions at the LHC at a centre-of-mass energy of 13 TeV. The data correspond to an integrated luminosity of 29.4 fb$^{-1}$. The $\mathrm{t} \bar{\mathrm{t}}$ decay products are reconstructed using the central CMS detector, while forward protons are measured in the CMS-TOTEM precision proton spectrometer. An observed (expected) upper bound on the production cross section of 0.59 (1.14) pb is set at 95% confidence level, for collisions of protons with fractional momentum losses between 2 and 20%.A search for the central exclusive production of top quark-antiquark pairs ($\mathrm{t\bar{t}}$) is performed for the first time using proton-tagged events in proton-proton collisions at the LHC at a centre-of-mass energy of 13 TeV. The data correspond to an integrated luminosity of 29.4 fb$^{-1}$. The $\mathrm{t\bar{t}}$ decay products are reconstructed using the central CMS detector, while forward protons are measured in the CMS-TOTEM precision proton spectrometer. An observed (expected) upper bound on the production cross section of 0.59 (1.14) pb is set at 95% confidence level, for collisions of protons with fractional momentum losses between 2 and 20%