Related papers: On algebraic twists with composite moduli
We introduce (quantum) twist automorphisms for upper cluster algebras and cluster Poisson algebras with coefficients. Our constructions generalize the twist automorphisms for quantum unipotent cells. We study their existence and their…
We provide the twisted Alexander polynomials of finite abelian covers over three-dimensional manifolds whose boundary is a finite union of tori. This is a generalization of a well-known formula for the usual Alexander polynomial of knots in…
The twisted $T$-adic exponential sum associated to a polynomial in one variable is studied. An explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the…
An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.
We investigate commutator operations on compatible uniformities of an algebra. We present a commutator operation for compatible uniformities of an algebra in a congruence-modular variety which extends the commutator on congruences, and…
We provide isomorphism results for Hopf algebras that are obtained as graded twistings of function algebras on finite groups by cocentral actions of cyclic groups. More generally , we also consider the isomorphism problem for…
We introduce the tautological rings of moduli stacks of twisted curves and establish some basic properties.
In this paper, we construct a large class of new simple modules over the twisted $N=2$ superconformal algebra. These new simple modules are restricted modules based on the simple modules over certain finite-dimensional solvable Lie…
We use twisted sheaves and their moduli spaces to study the Brauer group of a scheme. In particular, we (1) show how twisted methods can be efficiently used to re-prove the basic facts about the Brauer group and cohomological Brauer group…
Trace formulas are investigated in non-commutative integration theory. The main result is to evaluate the standard trace of a Takesaki dual and, for this, we introduce the notion of interpolator and accompanied boundary objects. The formula…
We introduce a notion of a (V,T)-module over a vertex algebra V for an arbitrary positive integer T, which is a generalization of a twisted V-module. Under some conditions on V, we construct an associative algebra A^{T}_{m}(V) for…
This paper is to study what we call twisted regular representations for vertex operator algebras. Let $V$ be a vertex operator algebra, let $\sigma_1,\sigma_2$ be commuting finite-order automorphisms of $V$ and let…
We introduce the notion of cyclic cohomology of an A-infinity algebra and show that the deformations of an A-infinity algebra which preserve an invariant inner product are classified by this cohomology. We use this result to construct some…
In this paper, we study the asymptotic behavior of the sum of twisted traces of self-dual or conjugate self-dual discrete automorphic representations of $\mathrm{GL}_n$ for the level aspect of principal congruence subgroups under some…
The automorphism group of a projective bundle P(E) over a simplicial toric variety is described when the bundle E is a direct sum of line bundles. Applications to study of moduli of complete intersections on toric varieties, including…
We apply the construction of the universal lower-bounded generalized twisted modules by the author to construct universal lower-bounded and grading-restricted generalized twisted modules for affine vertex (operator) algebras. We prove that…
Given a weight-one element $u$ of a vertex operator algebra $V$, we construct an automorphism of the category of generalized $g$-twisted modules for automorphisms $g$ of $V$ fixing $u$. We apply this construction to the case that $V$ is an…
We prove a theorem that allows one to count solutions to determinant equations twisted by a periodic weight with high uniformity in the modulus. It is obtained by using spectral methods of $\operatorname{SL}_2(\mathbb{R})$ automorphic forms…
We describe the role of algebraic extensions in the theory of commutative, unital normed algebras, with special attention to uniform algebras. We shall also compare these constructions and show how they are related to each other.
In this paper we study the behaviour of modules over finite dimensional algebras whose endomorphism algebra is a division ring. We show that there are finitely many such modules in the module category of an algebra if and only if the length…