Braided racks, Hurwitz actions and Nichols algebras with many cubic relations

We classify Nichols algebras of irreducible Yetter-Drinfeld modules over groups such that the underlying rack is braided and the homogeneous component of degree three of the Nichols algebra satisfies a given inequality. This assumption turns out to be equivalent to a factorization assumption on the Hilbert series. Besides the known Nichols algebras we obtain a new example. Our method is based on a combinatorial invariant of the Hurwitz orbits with respect to the action of the braid group on three strands.Comment: v2: 35 pages, 6 tables, 14 figure

Pointed Hopf Algebras with Triangular Decomposition: A Characterization of Multiparameter Quantum Groups

© 2016, The Author(s). In this paper, we present an approach to the definition of multiparameter quantum groups by studying Hopf algebras with triangular decomposition. Classifying all of these Hopf algebras which are of what we call weakly separable type over a group, we obtain a class of pointed Hopf algebras which can be viewed as natural generalizations of multiparameter deformations of universal enveloping algebras of Lie algebras. These Hopf algebras are instances of a new version of braided Drinfeld doubles, which we call asymmetric braided Drinfeld doubles. This is a generalization of an earlier result by Benkart and Witherspoon (Algebr. Represent. Theory 7(3) ? BC) who showed that two-parameter quantum groups are Drinfeld doubles. It is possible to recover a Lie algebra from these doubles in the case where the group is free abelian and the parameters are generic. The Lie algebras arising are generated by Lie subalgebras isomorphic to sl2

Hodge Star as Braided Fourier Transform

We study super-braided Hopf algebras $\Lambda$ primitively generated by finite-dimensional right crossed (or Drinfeld-Radford-Yetter) modules $\Lambda^1$ over a Hopf algebra $A$ which are quotients of the augmentation ideal $A^+$ under right multiplication and the adjoint coaction. Here super-bosonisation $\Omega=A\ltimes\Lambda$ provides a bicovariant differential graded algebra on $A$. We introduce $\Lambda_{max}$ providing the maximal prolongation, while the canonical braided-exterior algebra $\Lambda_{min}=B_-(\Lambda^1)$ provides the Woronowicz exterior calculus. In this context we introduce a Hodge star operator $\sharp$ by super-braided Fourier transform on $B_-(\Lambda^1)$ and left and right interior products by braided partial derivatives. Our new approach to the Hodge star (a) differs from previous approaches in that it is canonically determined by the differential calculus and (b) differs on key examples, having order 3 in middle degree on $k[S_3]$ with its 3D calculus and obeying the $q$-Hecke relation $\sharp^2=1+(q-q^{-1})\sharp$ in middle degree on $k_q[SL_2]$ with its 4D calculus. Our work also provided a Hodge map on quantum plane calculi and a new starting point for calculi on coquasitriangular Hopf algebras $A$ whereby any subcoalgebra $L\subseteq A$ defines a sub braided-Lie algebra and $\Lambda^1\subseteq L^*$ provides the required data $A^+\to \Lambda^1$.Comment: 36 pages latex 4 pdf figures; minor revision; added some background in calculus on quantum plane; improved the intro clarit

Thermophysical properties of the fe48cr15mo14c15b6y2 alloy in liquid state

In this work, the physical properties of Fe48Cr15Mo14C15B6Y2 alloy in liquid state at high temperature are studied. It was observed that the basic physical characteristics of the alloy, such as viscosity, electrical resistivity, and density, decrease with an increase of the temperature to 1700◦C. An abnormal increasing rate of viscosity for Fe48Cr15Mo14C15B6Y2 alloy in the temperature range from 1360 to 1550◦C was noted. The measurement of the electrical resistivity and density did not reveal any anomalies in the same temperature range. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.This research was funded by of the Ministry of Science and Higher Education of the Russian Federation in the framework of the Increase Competitiveness Program of NUST «MISiS» (grant number K2-2020-046). V.S.T., V.V.K. and V.V.V gratefully acknowledge the financial support made within the framework of state work No. FEUZ-0836-0020. Also, D.S.K. and J.V.I. gratefully acknowledge the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 897815 NanoSurf

Kondo flow invariants, twisted K-theory and Ramond-Ramond charges

We take a worldsheet point of view on the relation between Ramond-Ramond charges, invariants of boundary renormalization group flows and K-theory. In compact super Wess-Zumino-Witten models, we show how to associate invariants of the generalized Kondo renormalization group flows to a given supersymmetric boundary state. The procedure involved is reminiscent of the way one can probe the Ramond-Ramond charge carried by a D-brane in conformal field theory, and the set of these invariants is isomorphic to the twisted K-theory of the Lie group. We construct various supersymmetric boundary states, and we compute the charges of the corresponding D-branes, disproving two conjectures on this subject. We find a complete agreement between our algebraic charges and the geometry of the D-branes.Comment: 58 pages. V4 : Problem with the bibliography correcte

Twists of rational Cherednik algebras

The main result of the paper is that braided Cherednik algebras introduced by the first two authors are cocycle twists of rational Cherednik algebras. This gives a new construction of mystic reflection groups and a new proof that such groups have Artin-Schelter regular rings of quantum polynomial invariants. Furthermore, the main result leads to a construction of finite-dimensional representations of braided Cherednik algebras. In this first version of the paper, we give a full proof of the main result and sketch the application to representations of braided Cherednik algebras