Related papers: A note on Azumaya algebras and one-forms

We consider the general circumstance of an Azumaya algebra $A$ of degree $n$ over a locally ringed topos $(\mathbf{X}, {\mathcal{O}}_{\mathbf{ X}})$ where the latter carries a (possibly trivial) involution, denoted $\lambda$. This…

We study Morita theory of twisted sheaves on $\mu_{n}$-gerbes of line bundles $\mathscr{X}$. In this context, we find explicit equivalent conditions for when two Azumaya algebras on $\mathscr{X}$ are Morita equivalent. Additionally, we…

Atiyah and Hirzebruch gave examples ofeven degree torsion classes in the singularcohomology of a smooth complex projective manifold, which arenot Poincar\'{e} dual to an algebraiccycle. We notice that the order ofthese classes are small…

This paper establishes an isomorphism between endomorphism algebras from the wrapped Fukaya category of a type of punctured surface, and the class of A-infinity algebras related to bordered knot Floer homology, called star algebras, which…

A class of noncommutative spaces, named `soft noncommutative schemes via toric geometry', are constructed and the mathematical model for (dynamical/nonsolitonic, complex algebraic) D-branes on such a noncommutative space, following…

Gelfand, Retakh, Serconek and Wilson, in \cite{GRSW}, defined a graded algebra $A_\Gamma$ attached to any finite ranked poset $\Gamma$ - a generalization of the universal algebra of pseudo-roots of noncommutative polynomials. This algebra…

Comparing the module categories of an algebra and of the endomorphism algebra of a given support $\tau$-tilting module, we give a generalization of the Brenner-Butler's tilting theorem in the framework of $\tau$-tilting theory. Afterwards…

We use an idea of Rosenberg to prove a reconstruction theorem for abelian categories of alpha-twisted quasi-coherent sheaves on quasi-compact and quasi-separated schemes X when alpha is in the Brauer group of X. By applying the work of…

The goal of this note is to give an explicit formula for the residues of twists of the matrix algebra in terms of the twisting cocycle. Combined with the Fixed Point Theorem for actions of finite groups on affine buildings, this leads to a…

Let $X$ be a smooth affine symplectic variety over $\mathbb{Z}/p\mathbb{Z},$ and let $A_1$ be an Azumaya algebra over $X.$ In this note we show that if $A$ is a deformation quantization of $A_1$ over $\mathbb{Z}/p^n\mathbb{Z}$, then any…

We study moduli spaces and moduli stacks for representations of associative algebras in Azumaya algebras, in rather general settings. We do not impose any stability condition and work over arbitrary ground rings, but restrict attention to…

In this paper, we study Azumaya algebras and Brauer groups in derived algebraic geometry. We establish various fundamental facts about Brauer groups in this setting, and we provide a computational tool, which we use to compute the Brauer…

We identify a class of smooth Banach *-algebras that are differential subalgebras of commutative C*-algebras whose openness of multiplication is completely determined by the topological stable rank of the target C*-algebra. We then show…

We study the slice filtration for the K-theory of a sheaf of Azumaya algebras A, and for the motive of a Severi-Brauer variety, the latter in the case of a central simple algebra of prime degree over a field. Using the Beilinson-Lichtenbaum…

Here, I study the problem of classification of non-split supermanifolds having as retract the split supermanifold $(M,\Omega)$, where $\Omega$ is the sheaf of holomorphic forms on a given complex manifold $M$ of dimension $> 1$. I propose a…

We study the six-dimensional solvmanifolds that admit complex structures of splitting type classifying the underlying solvable Lie algebras. In particular, many complex structures of this type exist on the Nakamura manifold $X$, and they…

Let k be a base commutative ring, R a commutative ring of coefficients, X a quasi-compact quasi-separated k-scheme, A a sheaf of Azumaya algebras over X of rank r, and Hmo(R) the category of noncommutative motives with R-coefficients.…

Let $X$ be an equivariant embedding of a connected reductive group $G$ over an algebraically closed field $k$ of positive characteristic. Let $B$ denote a Borel subgroup of $G$. A $G$-Schubert variety in $X$ is a subvariety of the form…

Let G be a group and let W be an algebra over a field K. We will say that W is a G-graded twisted algebra if W can be written as a direct sum over the elements of G of one dimensional K-vector spaces. It is also assumed that W has no…

In this article, we consider algebras $\mathcal{A}$ of non-formal pseudodifferential operators over $S^1$ which contain $C^\infty(S^1),$ understood as multiplication operators. We apply a construction of Chern-Weil type forms in order to…