Boolean powers were introduced by Foster [5]. It was noticed by Jónsson in the review of [6], and further elaborated by Banaschewski and Nelson [1], that the Boolean power of an algebra A by a Boolean algebra B can be described as the algebra of continuous functions from the Stone space of B to A, where A has the discrete topology. It follows that a Boolean power of the group Z is an `-group ge...

If k is a field and R commutative k-algebra, we explore the question of when ring DR|k k-linear differential operators on isomorphic to its opposite ring. Under mild hypotheses, prove this case whenever Gorenstein local or invariants. As key step in proof show that many cases interest canonical modules admit right D-module structures.

We study combinatorial aspects of the representation theory of the 0-Hecke algebra Hn(0), a deformation of the group algebra of the symmetric group Sn. We study the action of Hn(0) on the polynomial ring in n variables. We show that the coinvariant algebra of this action naturally carries the regular representation of Hn(0), giving an analogue of the well-known result for the symmetric group by...

We provide a common generalization of the Springer map and quiver-graded Springer map due to Lusztig, called generalized quiver-graded Springer map associated to generalized quiver representations introduced by Derksen and Weyman. Following Chriss and Ginzburg for any equivariant projective map π : E → V , there is an algebra structure on the equivariant Borel-Moore homology of Z = E ×V E, we c...

We show a complete classification of faithful representations the 2 + 1 space-times Galilean Lie algebra on polynomial ring in three variables, where actions are given by derivations with coefficients degree at most one. In particular, all such explicitly constructed and classified one parameter. more general setting we that, respect to nonzero abelian ideal finite-dimensional algebra, there is...

On any set X may be defined the free algebra R〈X〉 (respectively, free commutative algebra R[X]) with coefficients in a ring R. It may also be equivalently described as the algebra of the free monoid X∗ (respectively, free commutative monoid M (X)). Furthermore, the algebra of differential polynomials R{X} with variables inX may be constructed. The main objective of this contribution is to provi...

For any normal commutative Hopf subalgebra K = k of a semisimple Hopf algebra we describe the ring inside kG obtained by the restriction of H-modules. If G = Zp this ring determines a fusion ring and we give a complete description for it. The case G = Zpn and some other applications are presented.

We study classes of modules over a commutative ring which allow to do homological algebra relative to such a class. We classify those classes consisting of injective modules by certain subsets of ideals. When the ring is Noetherian the subsets are precisely the generization closed subsets of the spectrum of the ring.

Introduction. The main objects of study in this paper are the commutative separable algebras over a commutative ring. Noncommutative separable algebras have been studied in [2]. Commutative separable algebras have been studied in [1] and in [2], [6] where the main ideas are based on the classical Galois theory of fields. This paper depends heavily on these three papers and the reader should con...

Let the reductive group G act on the finitely generated commutative k-algebra A. We ask if the finite generation property of the ring of invariants extends to the full cohomology ring. We confirm this when the action on A is replaced by the ‘contracted’ action on the Grosshans graded ring grA, provided the characteristic of k is large.