58,134 research outputs found
Cocommutative Calabi-Yau Hopf algebras and deformations
The Calabi-Yau property of cocommutative Hopf algebras is discussed by using
the homological integral, a recently introduced tool for studying infinite
dimensional AS-Gorenstein Hopf algebras. It is shown that the skew-group
algebra of a universal enveloping algebra of a finite dimensional Lie algebra
\g with a finite subgroup of automorphisms of \g is Calabi-Yau if and
only if the universal enveloping algebra itself is Calabi-Yau and is a
subgroup of the special linear group SL(\g). The Noetherian cocommutative
Calabi-Yau Hopf algebras of dimension not larger than 3 are described. The
Calabi-Yau property of Sridharan enveloping algebras of finite dimensional Lie
algebras is also discussed. We obtain some equivalent conditions for a
Sridharan enveloping algebra to be Calabi-Yau, and then partly answer a
question proposed by Berger. We list all the nonisomorphic 3-dimensional
Calabi-Yau Sridharan enveloping algebras
A cusp electron gun for millimeter wave gyrodevices
The experimental results of a thermionic cusp electron gun, to drive millimeter and submillimeter wave harmonic gyrodevices, are reported in this paper. Using a "smooth" magnetic field reversal formed by two coils this gun generated an annular-shaped, axis-encircling electron beam with 1.5 A current, and an adjustable velocity ratio alpha of up to 1.56 at a beam voltage of 40 kV. The beam cross-sectional shape and transported beam current were measured by a witness plate technique and Faraday cup, respectively. These measured results were found to be in excellent agreement with the simulated results using the three-dimensional code MAGIC
Calabi-Yau coalgebras
We provide a construction of minimal injective resolutions of simple
comodules of path coalgebras of quivers with relations. Dual to Calabi-Yau
condition of algebras, we introduce the Calabi-Yau condition to coalgebras.
Then we give some descriptions of Calabi-Yau coalgebras with lower global
dimensions. An appendix is included for listing some properties of cohom
functors
Dualities of artinian coalgebras with applications to noetherian complete algebras
A duality theorem of the bounded derived category of quasi-finite comodules
over an artinian coalgebra is established. Let be a noetherian complete
basic semiperfect algebra over an algebraically closed field, and be its
dual coalgebra. If is Artin-Schelter regular, then the local cohomology of
is isomorphic to a shift of twisted bimodule with
a coalgebra automorphism. This yields that the balanced dualinzing
complex of is a shift of the twisted bimodule . If
is an inner automorphism, then is Calabi-Yau
CP Violation in Fermion Pair Decays of Neutral Boson Particles
We study CP violation in fermion pair decays of neutral boson particles with
spin 0 or 1. We study a new asymmetry to measure CP violation in decays and discuss the possibility of measuring it
experimentally. For the spin-1 particles case, we study CP violation in the
decays of to octet baryon pairs. We show that these decays can
be used to put stringent constraints on the electric dipole moments of
, and .Comment: 14p, OZ-93/22, UM-93/89, OITS 51
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