Brauer–Clifford Group of ($$\varvec{S,{{\mathcal {G}}},H}$$)-Azumaya Algebras

2020 ◽  
Vol 30 (3) ◽  
Author(s):  
Thomas Guédénon
Keyword(s):  
Azumaya Algebras ◽  
Clifford Group

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.

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.

scholarly journals Construction of Polygonal Color Codes from Hyperbolic Tesselations

2020 ◽  
Vol 21 (1) ◽  
pp. 43
Author(s):  
Waldir S. Soares Jr ◽  
E. B. Silva ◽  
Emerson J. Vizentim ◽  
Franciele P. B. Soares
Keyword(s):  
Hyperbolic Geometry ◽  
Minimum Distance ◽  
Current Work ◽  
Clifford Group

This current work propose a technique to generate polygonal color codes in the hyperbolic geometry environment. The color codes were introduced by Bombin and Martin-Delgado in 2007, and the called triangular color codes have a higher degree of interest because they allow the implementation of the Clifford group, but they encode only one qubit. In 2018 Soares e Silva extended the triangular codes to the polygonal codes, which encode more qubits. Using an approach through hyperbolic tessellations we show that it is possible to generate Hyperbolic Polygonal codes, which encode more than one qubit with the capacity to implement the entire Clifford group and also having a better coding rate than the previously mentioned codes, for the color codes on surfaces with boundary with minimum distance d = 3.

Stability of unitary SK1 of Azumaya algebras

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