We initiate the systematic study of endomorphism algebras of permutation modules and show they are obtainable by a descent from a certain generic Hecke algebra, infinite-dimensional in general, coming from the universal enveloping algebra of gl n (or sln). The endomorphism algebras and the generic algebras are cellular (in the latter case, of profinite type in the sense of R.M. Green). We give ...

For certain graphs, we can associate a universal C*-algebra, which encodes the information of the graph algebraically. In this paper we examine the relationships between products of graphs and their associated C*-algebras. We present the underlying theory of associating a C*-algebra to a direct graph as well as to a higher rank graph. We then provide several isomorphisms relating C*-algebras of...

A sovereign monoidal category is an autonomous monoidal category endowed with the choice of an autonomous structure and an isomorphism of monoidal functors between the associated left and right duality functors. In this paper we define and study the algebraic counterpart of sovereign monoidal categories: cosovereign Hopf algebras. In this framework we find a categorical characterization of invo...

In this paper we prove that in prime characteristic there is a functor −p-Leib from the category of diassociative algebras to the category of restricted Leibniz algebras, generalizing the functor from associative algebras to restricted Lie algebras. Moreover we define the notion of restricted universal enveloping diassociative algebra Udp(g) of a restricted Leibniz algebra g and we show that Ud...

In recent work of T. Cassidy and the author, a notion of complete intersection was defined for (non-commutative) regular skew polynomial rings, defining it using both algebraic and geometric tools, where the commutative definition is a special case. In this article, we extend the definition to a larger class of algebras that contains regular graded skew Clifford algebras, the coordinate ring of...

Differential calculi of Poincaré-Birkhoff-Witt type on universal enveloping algebras of Lie algebras g are defined. This definition turns out to be independent of the basis chosen in g. The role of automorphisms of g is explained. It is proved that no differential calculus of PoincaréBirkhoff-Witt type exists on semi-simple Lie algebras. Examples are given, namely gln, Abelian Lie algebras, the...

Built on the foundations laid by Peirce, Schröder and others in the 19th century, the modern development of relation algebras started with the work of Tarski and his colleagues [21, 22]. They showed that relation algebras can capture strong rst-order theories like ZFC, and so their equational theory is undecidable. The less expressive classWA of weakly associative relation algebras were introd...

We determine the Kac quotient and RFD (residually finite dimensional) for Hopf * -algebras associated to universal orthogonal quantum groups.

Let C be a (small) category and let F : C −→ Malgf be a functor, where Malgf is the category of finite-dimensional measured algebras over a field k (or Frobenius algebras). We construct a universal Hopf algebra Aaut(F ) such that F factorizes through a functor F : C −→ Mcoalgf(Aaut(F )), where Mcoalgf(Aaut(F )) is the category of finite-dimensional measured Aaut(F )-comodule algebras. This gene...

We construct twisting elements for module algebras of restricted two-parameter quantum groups from factors of their R-matrices. We generalize the theory of Giaquinto and Zhang to universal deformation formulas for categories of module algebras and give examples arising from R-matrices of two-parameter quantum groups.