scholarly journals The automorphisms of generalized cyclic Azumaya algebras

2021 ◽  
Vol 225 (4) ◽  
pp. 106540
Author(s):  
S. Pumplün
Keyword(s):  
Azumaya Algebras

scholarly journals The resolution property via Azumaya algebras

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Siddharth Mathur
Keyword(s):  
Azumaya Algebras ◽  
Algebraic Space ◽  
Local Methods ◽  
Artin Stacks ◽  
Resolution Property

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. Our construction passes through the case of tame Artin gerbes, tame Artin curves, and algebraic space surfaces, each of which we establish independently.

Stability of unitary SK1 of Azumaya algebras

2011 ◽  
Vol 98 (1) ◽  
pp. 19-23
Author(s):  
Roozbeh Hazrat
Keyword(s):  
Azumaya Algebras

scholarly journals Derived Azumaya algebras and twisted K-theory

2019 ◽  
Vol 351 ◽  
pp. 761-803 ◽  
Author(s):  
Tasos Moulinos
Keyword(s):  
Azumaya Algebras ◽  
K Theory

scholarly journals Cancellative semigroup rings which are Azumaya algebras

1988 ◽  
Vol 117 (2) ◽  
pp. 290-296 ◽  
Author(s):  
J Okninski ◽  
F Van Oystaeyen
Keyword(s):  
Cancellative Semigroup ◽  
Semigroup Rings ◽  
Azumaya Algebras

scholarly journals On separable cyclic extensions of rings

1982 ◽  
Vol 32 (2) ◽  
pp. 165-170 ◽  
Author(s):  
George Szeto ◽  
Yuen-Fat Wong
Keyword(s):  
Commutative Ring ◽  
Quaternion Algebra ◽  
Cyclic Extension ◽  
Noncommutative Ring ◽  
Azumaya Algebras ◽  
Galois Extensions

AbstractThe quaternion algebra of degree 2 over a commutative ring as defined by S. Parimala and R. Sridharan is generalized to a separable cyclic extension B[j] of degree n over a noncommutative ring B. A characterization of such an extension is given, and a relation between Azumaya algebras and Galois extensions for B[j] is also obtained.

scholarly journals Invariant bilinear forms of algebras given by faithfully flat descent

2015 ◽  
Vol 17 (02) ◽  
pp. 1450009 ◽  
Author(s):  
E. Neher ◽  
A. Pianzola ◽  
D. Prelat ◽  
C. Sepp
Keyword(s):  
Lie Algebras ◽  
Ad Hoc ◽  
Bilinear Forms ◽  
Affine Lie Algebras ◽  
Azumaya Algebras

The existence of nondegenerate invariant bilinear forms is one of the most important tools in the study of Kac–Moody Lie algebras and extended affine Lie algebras. In practice, these forms are created, or shown to exist, either by assumption or in an ad hoc basis. The purpose of this work is to describe the nature of the space of invariant bilinear forms of certain algebras given by faithfully flat descent (which includes the affine Kac–Moody Lie algebras, as well as Azumaya algebras and multiloop algebras) within a functorial framework. This will allow us to conclude the existence, uniqueness and nature of invariant bilinear forms for many important classes of algebras.

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