Related papers: Free algebras via monoidal envelopes

In hep-th/0010293 Kapustin and Orlov introduce the notion of an OPE-algebra and propose that it formalizes conformal field theories in the same way as vertex algebras formalize chiral algebras, i.e. the subalgebras of holomorphic fields of…

We give an especially simple proof of a theorem in graph theory that forms the key part of the solution to a problem in commutative algebra, on how to characterize the integral closure of a polynomial ring generated by quadratic monomials.

It has been proved by the author [arXiv: 2404.19433] that the Arens-Michael envelope of a solvable Lie algebra is a homological epimorphism. We show here that for algebras of analytic functionals on a connected complex Lie group the…

A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…

We show that the quantised function algebra O_e(G) of a simply-connected semisimple algebraic group G at a root of unity is a free module over the subring isomorphic to O(G).

We provide a construction of free factorization algebras in algebraic geometry and link factorization homology of a scheme with coefficients in a free factorization algebra to the homology of its (unordered) configuration spaces. As an…

In this paper we prove that, in the category of chain complexes, partial algebras can be functorially replaced by quasi-isomorphic algebras. In particular, partial algebras contain all of the important homological and homotopical…

We define a notion of cofibration among n-categories and show that the cofibrant objects are exactly the free ones, that is those generated by polygraphs.

Let $P(N,V)$ denote the vector space of polynomials of maximal degree less than or equal to $N$ in $V$ independent variables. This space is preserved by the enveloping algebra generated by a set of linear, differential operators…

Let D^n be the closed unit polydisk in C^n. Consider the ring C_r of complex-valued continuous functions on D^n that are real symmetric, that is, f(z)=(f(z^*))^* for all z in D^n. It is shown that C_r is projective free, that is, finitely…

We consider a space of complex polynomials of degree $n\ge 3$ with $n-1$ distinguished periodic orbits. We prove that the multipliers of these periodic orbits considered as algebraic functions on that space, are algebraically independent…

We construct a symmetric monoidal category $LIE^{MC}$ whose objects are shifted L-infinity algebras equipped with a complete descending filtration. Morphisms of this category are "enhanced" infinity morphisms between shifted L-infinity…

We investigate the Galois coverings of piecewise algebras and more particularly their behaviour under derived equivalences. Under a technical assumption which is satisfied if the algebra is derived equivalent to a hereditary algebra, we…

We prove that for every natural number n there exists a natural number N(n) such that every multilinear skew-symmetric polynomial on N(n) or more variables which vanishes in the free associative algebra vanishes as well in any n-generated…

We prove that if two homomorphisms from O_{\infty} to a purely infinite simple C*-algebra have the same class in KK-theory, and if either both are unital or both are nonunital, then they are approximately unitarily equivalent. It follows…

In this paper, we consider free transposed Poisson algebra and free F-manifold algebra with an additional metabelian identity. We construct a linear basis for both free metabelian transposed Poisson algebra and free metabelian F-manifold…

We prove that the group of tame automorphisms of a free Lie algebra (as well as of a free anticommutative algebra) rank 3 over an arbitrary integral domain has the structure of an amalgamated free product. We construct an example of a wild…

In this note, we give a new characterization for an algebra to be $\qo$-compact in terms of {\em super-product operations} on the lattice of congruences of the relative free algebra.

Hom-algebras are generalizations of algebras obtained using a twisting by a linear map. But there is a priori a freedom on where to twist. We enumerate here all the possible choices in the Lie and associative categories and study the…

For $\Lambda$ the category of free opetopic algebras, we construct a model structure \emph{\`a la Cisinski} on the category of presheaves over $\Lambda$, and show that is is equivalent to opetopic complete Segal spaces. This generalizes the…