Results 31 to 40 of about 633,805 (104)

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
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The resolution property via Azumaya algebras [PDF]

Journal für die reine und angewandte Mathematik (Crelles Journal), 2021
Abstract Using formal-local methods, we prove that a separated and normal tame Artin surface has the resolution property. By proving that normal tame Artin stacks can be rigidified, we ultimately reduce our analysis to establishing the existence of Azumaya algebras.
openaire   +3 more sources

Endomorphisms of quantized Weyl algebras

, 2010
Belov-Kanel and Kontsevich conjectured that the group of automorphisms of the n'th Weyl algebra and the group of polynomial symplectomorphisms of C^2 are canonically isomorphic.
A. Belov-Kanel, A. Joseph, E. Backelin, Erik Backelin, J. Christensen, J. Dixmier, Jung, K. Adjamagbo, L. Makar-Limanov, M. Kontsevich, M. Kontsevich, S. Majid, Y. Tsuchimoto   +12 more
core   +1 more source

The index of projective families of elliptic operators

, 2005
An index theory for projective families of elliptic pseudodifferential operators is developed. The topological and the analytic index of such a family both take values in twisted K-theory of the parametrizing space, X.
Alvarez, Berline, Dixmier, Donovan, Grothendieck, Isadore M Singer, Murray, Raeburn, Richard B Melrose, Rieffel, Rosenberg, Rosenberg, Tsuboi, Varghese Mathai   +13 more
core   +2 more sources

On ring homomorphisms of Azumaya algebras [PDF]

, 2005
The main theorem (Theorem 4.1) of this paper claims that any ring morphism from an Azumaya algebra of constant rank over a commutative ring to another one of the same constant rank and over a reduced commutative ring induces a ring morphism between the ...
Adjamagbo, Kossivi, Charbonnel, Jean-Yves, Essen, Arno Van Den   +2 more
core   +2 more sources

$K$-Theory of Azumaya algebras

Irish Mathematical Society Bulletin, 2010
For an Azumaya algebra $A$ which is free over its centre $R$, we prove that the $K$-theory of $A$ is isomorphic to $K$-theory of $R$ up to its rank torsion. We observe that a graded central simple algebra, graded by an abelian group, is a graded Azumaya algebra and it is free over its centre.
openaire   +2 more sources

Braidings on the category of bimodules, Azumaya algebras and epimorphisms of rings

, 2012
Let $A$ be an algebra over a commutative ring $k$. We prove that braidings on the category of $A$-bimodules are in bijective correspondence to canonical R-matrices, these are elements in $A\ot A\ot A$ satisfying certain axioms. We show that all braidings
Agore, A. L., Caenepeel, S., Militaru, G.   +2 more
core   +1 more source

Centers and Azumaya loci of finite $W$-algebras

, 2020
In this paper, we study the center $Z$ of the finite $W$-algebra $\mathcal{T}(\mathfrak{g},e)$ associated with a semi-simple Lie algebra $\mathfrak{g}$ over an algebraically closed field $\mathds{k}$ of characteristic $p\gg0$, and an arbitrarily given ...
Shu, Bin, Zeng, Yang
core  

D-branes and Azumaya noncommutative geometry: From Polchinski to Grothendieck [PDF]

, 2010
We review first Azumaya geometry and D-branes in the realm of algebraic geometry along the line of Polchinski-Grothendieck Ansatz from our earlier work and then use it as background to introduce Azumaya $C^{\infty}$-manifolds with a fundamental module ...
Liu, Chien-Hao, Yau, Shing-Tung
core  

Counterexamples in involutions of Azumaya algebras

Journal of Algebra
21 ...
Uriya First, Ben Williams
openaire   +2 more sources