Results 31 to 40 of about 2,189 (114)

Projective Dirac Operators, Twisted K-Theory and Local Index Formula [PDF]

, 2011
We construct a canonical noncommutative spectral triple for every oriented closed Riemannian manifold, which represents the fundamental class in the twisted K-homology of the manifold.
Zhang, Dapeng
core   +4 more sources

On Hopf DeMeyer‐Kanzaki Galois extensions

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 26, Page 1627-1632, 2003., 2003
Let H be a finite‐dimensional Hopf algebra over a field k, B a left H‐module algebra, and H∗ the dual Hopf algebra of H. For an H∗‐Azumaya Galois extension B with center C, it is shown that B is an H∗‐DeMeyer‐Kanzaki Galois extension if and only if C is a maximal commutative separable subalgebra of the smash product B#H.
George Szeto, Lianyong Xue
wiley   +1 more source

Azumaya locus over certain quantum symplectic spaces II

Comptes Rendus. Mathématique
This article undertakes an exploration of a particular variant of multiparameter quantum symplectic algebras, focusing specifically on the quantum Heisenberg algebra at the roots of unity.
Mukherjee, Snehashis
doaj   +1 more source

On characterizations of a center Galois extension

International Journal of Mathematics and Mathematical Sciences, 2000
Let B be a ring with 1,  C the center of B,  G a finite automorphism group of B, and BG the set of elements in B fixed under each element in G. Then, it is shown that B is a center Galois extension of BG (that is, C is a Galois algebra over CG with ...
George Szeto, Lianyong Xue
doaj   +1 more source

Azumaya Objects in Triangulated Bicategories

, 2013
We introduce the notion of Azumaya object in general homotopy-theoretic settings. We give a self-contained account of Azumaya objects and Brauer groups in bicategorical contexts, generalizing the Brauer group of a commutative ring.
A Baker, A Baker, A Neeman, B Day, B Shipley, B Toën, EM Vitale, F Borceux, J Rickard, JP May, M Auslander, M Auslander, M Hovey, MA Knus, MA Mandell, N Gurski, PM Cohn, S Schwede, S Schwede, S Schwede   +19 more
core   +1 more source

There are enough Azumaya algebras on surfaces [PDF]

Mathematische Annalen, 2001
Using Maruyama's theory of elementary transformations, I show that the Brauer group surjects onto the cohomological Brauer group for separated geometrically normal algebraic surfaces. As an application, I infer the existence of nonfree vector bundles on proper normal algebraic surfaces.
openaire   +2 more sources

Modular representations of Loewy length two

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 70, Page 4399-4408, 2003., 2003
Let G be a finite p‐group, K a field of characteristic p, and J the radical of the group algebra K[G]. We study modular representations using some new results of the theory of extensions of modules. More precisely, we describe the K[G]‐modules M such that J2M = 0 and give some properties and isomorphism invariants which allow us to compute the number ...
M. E. Charkani, S. Bouhamidi
wiley   +1 more source

Rings That Are Morita Equivalent to Their Opposites

, 2015
We consider the following problem: Under what assumptions do one or more of the following are equivalent for a ring $R$: (A) $R$ is Morita equivalent to a ring with involution, (B) $R$ is Morita equivalent to a ring with an anti-automorphism, (C) $R$ is ...
First, Uriya A.
core   +1 more source

On Hopf Galois Hirata extensions

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 64, Page 4033-4039, 2003., 2003
Let H be a finite‐dimensional Hopf algebra over a field K, H* the dual Hopf algebra of H, and B a right H*‐Galois and Hirata separable extension of BH. Then B is characterized in terms of the commutator subring VB(BH) of BH in B and the smash product VB(BH)#H. A sufficient condition is also given for B to be an H*‐Galois Azumaya extension of BH.
George Szeto, Lianyong Xue
wiley   +1 more source

The Galois algebras and the Azumay Galois extensions

International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 1, Page 37-42, 2002., 2002
Let B be a Galois algebra over a commutative ring R with Galois group G, C the center of B, K = {g ∈ G | g(c) = c for all c ∈ C}, Jg{b ∈ B | bx = g(x)b for all x ∈ B} for each g ∈ K, and BK = (⊕∑g∈K Jg). Then BK is a central weakly Galois algebra with Galois group induced by K.
George Szeto, Lianyong Xue
wiley   +1 more source