Related papers: A post-group theoretic perspective on the operator…
In this paper, we provide a generalized version of the Voiculescu theorem for normal operators by showing that, in a von Neumann algebra with separable pre-dual and a faithful normal semifinite tracial weight $\tau$, a normal operator is an…
We explain the notion of a post-Lie algebra and outline its role in the theory of Lie group integrators.
We introduce two 2-variables transforms: the partial bi-free S-transform and the partial bi-free T-transform. These transforms are the analogues for the bi-multiplicative and respectively for the additive-multiplicative bi-free convolution…
The process of replacing an arbitrary Boolean function by a bijective one, a fundamental tool in reversible computing and in cryptography, is interpreted algebraically as a particular instance of a certain group homomorphism from the X-fold…
In this paper we review some of the fundamental properties of the free group and give a detailed account of Stallings's theory of automata, a geometric interpretation of its subgroups that has been (and still is) immensely fruitful, both as…
In 1999 Chas and Sullivan showed that the homology of the free loop space of an oriented manifold admits the structure of a Batalin-Vilkovisky algebra. In this paper we give a direct description of this Batalin-Vilkovisky algebra in the…
This paper defines the algebraic structure of tracial post-Lie-Rinehart algebras and describes the free object in this category. Post-Lie-Rinehart algebras is a generalisation of pre-Lie-Rinehart algebras, and of post-Lie algebroids.
The main goal of this paper is to study the structure of the graded algebra associated to a valuation. More specifically, we prove that the associated graded algebra ${\rm gr}_v(R)$ of a subring $(R,\mathfrak{m})$ of a valuation ring…
In joint work with M. Hopkins and C. Teleman we find a new description of the Verlinde algebra associated to a compact Lie group. In this expository account we describe twisted K-theory, prove the theorem for the group SU(2), and motivate…
In this paper, using extension theory and cohomological approach we introduce the notion of the obstruction class for an inner post-Lie algebra being induced by a Rota-Baxter operator, and show that an inner post-Lie algebra is induced by a…
In this paper, we study the C-enriched pre-Lie operad defined by Calaque and Willwacher for any Hopf cooperad C to produce conceptual constructions of the operads acting on various deformation complexes. Maps between Hopf cooperads lead to…
We present the analytic foundation of a unified B-D-F extension functor $\operatorname{Ext}_\tau$ on the category of noncommutative smooth algebras, for any Fr\'echet operator ideal $\Cal K_\tau$. Combining the techniques devised by Arveson…
We investigate deformations of skew group algebras that arise from a finite cyclic group acting on a polynomial ring in positive characteristic, where characteristic divides the order of the group. We allow deformations which deform both…
The goal of this note is to show that the left $\chi$-coalgebra, which is an additional structure on one of the coefficients used in the construction of the cyclic operator for the cyclic sets that generalises the twisted nerve of a group…
In the present paper we introduce the generalized inverse operators which have an interesting role in operator theory. We establish Douglas' factorization theorem type for Hilbert pro-$C^{\ast}$-module. We introduce the notion of atomic…
We introduce the notions of open-closed field algebra and open-closed field algebra over a vertex operator algebra V. In the case that V satisfies certain finiteness and reductivity conditions, we show that an open-closed field algebra over…
We define an extension of the polynomial calculus on a W*-probability space by introducing an abstract algebra which contains polynomials. This extension allows us to define transition operators for additive and multiplicative free…
Let S be a compact connected oriented surface, whose boundary is connected or empty. A homology cylinder over the surface S is a cobordism between S and itself, homologically equivalent to the cylinder over S. The Y-filtration on the monoid…
We apply the effective integration theory of Lie-graph algebras, developed recently by the authors, to the deformation and homotopy theories of types of bialgebras, that is structures controlled by a properad, like associative bialgebras,…
We consider the structure of algebra of operators, acting in $n-$fold tensor product space, which are partially transposed on the last term. Using purely algebraical methods we show that this algebra is semi-simple and then, considering its…