相关论文: Universal measuring coalgebras and R - transformat…

Universal enveloping Rota-Baxter algebras of preassociative and postassociative algebras are constructed. The question of Li Guo is answered: the pair of varieties (Rota-Baxter algebras of nonzero weight,postassociative algebras) is a…

For n even, we prove Pozhidaev's conjecture on the existence of associative enveloping algebras for simple n-Lie algebras. More generally, for n even and any (n+1)-dimensional n-Lie algebra L, we construct a universal associative enveloping…

Kashaev algebra associated to a surface is a noncommutative deformation of the algebra of rational functions of Kashaev coordinates. For two arbitrary complex numbers, there is a generalized Kashaev algebra. The relationship between the…

In this paper, W*-algebras are presented as canonical colimits of diagrams of matrix algebras and completely positive maps. In other words, matrix algebras are dense in W*-algebras.

We prove that if U_h(g) is a quasitriangular QUE algebra with universal R-matrix R, and O_h(G^*) is the quantized function algebra sitting inside U_h(g), then h log(R) belongs to the tensor square O_h(G^*) otimes O_h(G^*). This gives…

We introduce a diagram category, study its structure, and investigate some of its applications to the representation theory of Lie algebras and Lie superalgebras. The morphisms of the category, which contains a subcategory isomorphic to the…

We establish a canonical and unique tensor product for commutative monoids and groups in an infinity-category C which generalizes the ordinary tensor product of abelian groups. Using this tensor product we show that E_n-(semi)ring objects…

We define the notion of Y-algebroids, generalising the Lie, Courant, and exceptional algebroids that have been used to capture the local symmetry structure of type II string theory and M-theory compactifications to $D \geq 5$ dimensions.…

Over a field of characteristic zero, we show that the forgetful functor from the homotopy category of commutative dg algebras to the homotopy category of dg associative algebras is faithful. In fact, the induced map of derived mapping…

This paper extends the theory of universal measuring comonoids to modules and comodules in braided monoidal categories. We generalise the universal measuring comodule Q(M,N), originally introduced for modules over k-algebras when k is a…

We develop a new general framework for algebras and clones, called Universal Clone Algebra. Algebras and clones of finitary operations are to Universal Algebra what t-algebras and clone algebras are to Universal Clone Algebra. Clone…

We consider, for each exchange matrix B, a category of geometric cluster algebras over B and coefficient specializations between the cluster algebras. The category also depends on an underlying ring R, usually the integers, rationals, or…

A class of associative (super) algebras is presented, which naturally generalize both the symmetric algebra $Sym(V)$ and the wedge algebra $\wedge (V)$, where $V$ is a vector-space. These algebras are in a bijection with those subsets of…

We discuss the noncommutative generalizations of polynomial algebras which after appropriate completions can be used as coordinate algebras in various noncommutative settings, (noncommutative differential geometry, noncommutative algebraic…

An R-algebra A is called E(R)-algebra if the canonical homomorphism from A to the endomorphism algebra End_RA of the R-module {}_R A, taking any a in A to the right multiplication a_r in End_R A by a is an isomorphism of algebras. In this…

Some filtrations of the tensor product of a highest weight module and a lowest weight module over quantum group $U_q(\mathfrak g)$ are constructed in \cite{LZ:2009} and one can use them to define some ideals of the modified quantized…

For q generic or a primitive l-th root of unity, q-Witt algebras are described by means of q-divided power algebras. The structure of the universal q-central extension of the q-Witt algebra, the q-Virasoro algebra, is also determined. q-Lie…

Natural linear and coalgebra transformations of tensor algebras are studied. The representations of certain combinatorial groups are given. These representations are connected to natural transformations of tensor algebras and to the groups…

We show that the data needed for the method of the embedding tensor employed in gauging supergravity theories are precisely those of a Leibniz algebra (with one of its induced quotient Lie algebras embedded into a rigid symmetry Lie algebra…

We study quantization of a class of inhomogeneous Lie bialgebras which are crossproducts in dual sectors with Abelian invariant parts. This class forms a category stable under dualization and the double operations. The quantization turns…