The Brauer Group of Graded Azumaya Algebras. II: Graded Galois Extensions

1975 ◽  
Vol 204 ◽  
pp. 137 ◽  
Author(s):  
Lindsay N. Childs
Keyword(s):  
Brauer Group ◽  
Azumaya Algebras ◽  
Galois Extensions

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 Computing the Brauer group of graded Azumaya algebras from its subgroups

1986 ◽  
Vol 101 (2) ◽  
pp. 339-349 ◽  
Author(s):  
Margaret Beattie
Keyword(s):  
Brauer Group ◽  
Azumaya Algebras

scholarly journals The brauer group of central separable G-Azumaya algebras

1978 ◽  
Vol 54 (2) ◽  
pp. 516-525 ◽  
Author(s):  
Margaret Beattie
Keyword(s):  
Brauer Group ◽  
Azumaya Algebras

scholarly journals The Brauer group of graded Azumaya algebras

1973 ◽  
Vol 175 ◽  
pp. 299-299 ◽  
Author(s):  
L. N. Childs ◽  
G. Garfinkel ◽  
M. Orzech
Keyword(s):  
Brauer Group ◽  
Azumaya Algebras

Azumaya algebras and the brauer group of fpf rings

1985 ◽  
Vol 13 (2) ◽  
pp. 329-336 ◽  
Author(s):  
Stanley S. Page
Keyword(s):  
Brauer Group ◽  
Azumaya Algebras

scholarly journals Hopf-Galois extensions of algebras, the Miyashita-Ulbrich action, and Azumaya algebras

1989 ◽  
Vol 121 (2) ◽  
pp. 488-516 ◽  
Author(s):  
Yukio Doi ◽  
Mitsuhiro Takeuchi
Keyword(s):  
Azumaya Algebras ◽  
Galois Extensions

Brauer–Clifford Group of Lie–Rinehart Algebras

2022 ◽  
Vol 29 (01) ◽  
pp. 99-112
Author(s):  
Thomas Guédénon
Keyword(s):  
Differential Geometry ◽  
Commutative Ring ◽  
Lie Algebra ◽  
Commutative Algebra ◽  
Monoidal Category ◽  
Brauer Group ◽  
Azumaya Algebras ◽  
Symmetric Monoidal Category ◽  
Clifford Group

In this paper we define the notion of Brauer–Clifford group for [Formula: see text]-Azumaya algebras when [Formula: see text] is a commutative algebra and[Formula: see text] is a [Formula: see text]-Lie algebra over a commutative ring [Formula: see text]. This is the situation that arises in applications having connections to differential geometry. This Brauer–Clifford group turns out to be an example of a Brauer group of a symmetric monoidal category.

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