Related papers: Twisted doubling integrals for Brylinski-Deligne e…
We develop a Gauss decomposition approach to establish a Drinfeld type current presentation for Olshanski's twisted Yangians associated to the orthogonal Lie algebras (also called twisted Yangians of type AI), settling a longstanding open…
Twisted links are a generalization of classical links and correspond to stably equivalence classes of links in thickened surfaces. In this paper we introduce twisted intersection colorings of a diagram and construct two invariants of a…
We provide formulas for computing the discriminant of noncommutative algebras over central subalgebras in the case of Ore extensions and skew group extensions. The formulas follow from a more general result regarding the discriminants of…
We define group-twisted Alexander-Whitney and Eilenberg-Zilber maps for converting between bimodule resolutions of skew group algebras. These algebras are the natural semidirect products recording actions of finite groups by automorphisms.…
We study the notion of twisted conjugacy separability (essentially introduced in our previous paper for a proof of twisted version of Burnside-Frobenius theorem) and some related properties. We give examples of groups with and without this…
We study noncommutative principal bundles (Hopf-Galois extensions) in the context of coquasitriangular Hopf algebras and their monoidal category of comodule algebras. When the total space is quasi-commutative, and thus the base space…
It is well-known that the tensor product of two bialgebras constitutes the binary product in the category of cocommutative bialgebras and morphisms of bialgebras between them. In this paper, we extend this result to triangular bialgebras…
We introduce a new class of graded rings extending the class of generalized Weyl algebras. These rings are orders in crossed products of the most general type, and we introduce their basic structure theory. We provide an extensive list of…
In this paper, we established some integral formulas for and involving the noncentral Tanny-Dowling polynomials. These formulas are shown to be generalizations of some known results on the classical geometric polynomials.
We prove that suitable properties of the twists by Dirichlet characters of an L-function of degree 2 imply that its Euler product is of polynomial type.
We explicitly describe the derived Picard groups of symmetric representation-finite algebras of type $D$. In particular, we prove that these groups are generated by spherical twists along collections of $0$-spherical objects, the shift and…
A twisted covariant formulation of noncommutative self-dual gravity is presented. The formulation for constructing twisted noncommutative Yang-Mills theories is used. It is shown that the noncommutative torsion is solved at any order of the…
Historically, the study of graded (twisted or otherwise) Calabi--Yau algebras has meant the study of such algebras under an $\mathbb{N}$-grading. In this paper, we propose a suitable definition for a twisted $G$-graded Calabi-Yau algebra,…
We generalize the idea of "extension of Hamiltonian systems" -- developed in a series of previous articles -- which allows the explicit construction of Hamiltonian systems with additional non-trivial polynomial first integrals of…
In this paper, we introduce the new class of twisted $B$-splines and study some properties of these B-splines. We also investigate the system of twisted translates and the wavelets corresponding to these twisted $B$-splines.
We review the results of several of our papers about the procedure of extension of Hamiltonians, allowing the construction of families of superintegrable systems with non-trivial polynomial first integrals (or symmetry operators) of…
In this paper, we characterize all the finite dimensional algebras that are derived equivalent to an m-cluster tilted algebra of type A tilde. This generalizes a result of Bobonski and Buan [9].
In this paper, we initiate the study of C*-algebras endowed with a twisted action of a locally compact Abelian Lie group, and we construct a twisted crossed product, which is in general a nonassociative, noncommutative, algebra. The…
We describe a unifying framework for the systematic construction of integrable deformations of integrable $\sigma$-models within the Hamiltonian formalism. It applies equally to both the `Yang-Baxter' type as well as `gauged WZW' type…
We will introduce an operation "twisting" on Hochschild complex by analogy with Drinfeld's twisting operations. By using the twisting and derived bracket construction, we will study differential graded Lie algebra structures associated with…