Related papers: Groupoids, Frobenius algebras and Poisson sigma mo…

To each symmetric graded Frobenius superalgebra we associate a W-algebra. We then define a linear isomorphism between the trace of the Frobenius Heisenberg category and a central reduction of this W-algebra. We conjecture that this is an…

In the present paper by Frobenius algebra Y we mean a finite dimensional algebra possessing an associative and invertible (nondegenerate) form a scalar product, referred to as the Frobenius structure. The nondegenerate form has an inverse.…

We give a concise introduction to (discrete) algebras arising from \'etale groupoids, (aka Steinberg algebras) and describe their close relationship with groupoid C*-algebras. Their connection to partial group rings via inverse semigroups…

In the first part we study nearly Frobenius algebras. The concept of nearly Frobenius algebras is a generalization of the concept of Frobenius algebras. Nearly Frobenius algebras do not have traces, nor they are self-dual. We prove that the…

Categories of relations over a regular category form a family of models of quantum theory. Using regular logic, many properties of relations over sets lift to these models, including the correspondence between Frobenius structures and…

As we said in our previous work [4], the main idea of our research is to introduce a class of Lie groupoids by means of co-adjoint representation of a Lie groupoid on its isotropy Lie algebroid, which we called coadjoint Lie groupoids. In…

We describe a special class of representations of an inverse semigroup S on Hilbert's space which we term "tight". These representations are supported on a subset of the spectrum of the idempotent semilattice of S, called the "tight…

If $A$ is a finite-dimensional algebra graded by a group $G$, and $\sigma \in G$, we define a variant of paratrophic matrix associated with $A$ and $\sigma$, and we use it to characterize the $\sigma$-graded Frobenius property for $A$. We…

We present a new method, involving monads and comonads from category theory, to help establish a certain type of equivalence of subcategories. As a case study we consider the category of topological gradings of $C^*$-algebras over a fixed…

This paper is a sequel to arXiv:2307.13358 and arXiv:2308.16090. A construction associating a semialgebra with an algebra, subalgebra, and a coalgebra dual to the subalgebra played a central role in the author's book arXiv:0708.3398. In…

In order to study graded Frobenius algebras from a ring theoretical perspective, we introduce graded quasi-Frobenius rings, graded Frobenius rings and a shift-version of the latter ones, and we investigate the structure and representations…

We introduce a new class of algebras called Poisson orders. This class includes the symplectic reflection algebras of Etingof and Ginzburg, many quantum groups at roots of unity, and enveloping algebras of restricted Lie algebras in…

The `spider theorem' for a general Frobenius algebra $A$, classifies all maps $A^{\otimes m}\to A^{\otimes n}$ that are built from the operations and, in a graphical representation, represented by a {\it connected} diagram. Here the algebra…

In this paper we describe the the category of Lie algebras of group algebras and the category of Plesken Lie algebras and explore the categorical relations between them. Further we provide the examples of the Lie algebra of the group…

We consider Frobenius algebras and their bimodules in certain abelian monoidal categories. In particular we study the Picard group of the category of bimodules over a Frobenius algebra, i.e. the group of isomorphism classes of invertible…

The study of Frobenius algebras in the category $\mathbf{Rel}$ via their nerve functor into simplicial sets has been introduced recently. In this article, we focus on the particular case of effect algebras and pseudo effect algebras and…

We associate a graded monoidal supercategory $\mathcal{H}\mathit{eis}_{F,k}$ to every graded Frobenius superalgebra $F$ and integer $k$. These categories, which categorify a broad range of lattice Heisenberg algebras, recover many…

Generalising the well-known correspondence between two-sided adjunctions and Frobenius algebras, we establish a one-to-one correspondence between local adjunctions of C*-correspondences, as defined and studied in prior work with P. Clare…

We point out, and draw some consequences of, the fact that the Poisson Lie group G* dual to G=GL_n(C) (with its standard complex Poisson structure) may be identified with a certain moduli space of meromorphic connections on the unit disc…

We present a unified apoach to the study of separable and Frobenius algebras. The crucial observation is thsat both cases are related to the nonlinear equation $R^{12}R^{23}=R^{23}R^{13}=R^{13}R^{12}$, called the FS-equation. Given a…