We consider a tower of generalized rook monoid algebras over the field C of complex numbers and observe that the Bratteli diagram associated to this tower is a simple graph. We construct simple modules and describe Jucys-Murphy elements for generalized rook monoid algebras. Over an algebraically closed field k of positive characteristic p, utilizin...
In this paper, building on previous work by Lambert, Plagne and the third author, we study various aspects of the behavior of additive bases in a class of infinite abelian semigroups, which we term \em translatable \em semigroups. These include all numerical semigroups as well as all infinite abelian groups. We show that, for every such semigroup $...
Published in Lobachevskii Journal of Mathematics
The paper deals with the normal extensions of cancellative commutative semigroups and the Toeplitz algebras for those semigroups. By the Toeplitz algebra for a semigroup S one means the reduced semigroup C*-algebra Cr*(S). We study the normal extensions of cancellative commutative semigroups by the additive group ℤn of integers modulo n. Moreover, ...
We describe a strategy for the construction of finitely generated G-equivariant Z-graded modules M over the exterior algebra for a finite group G. By an equivariant version of the BGG correspondence, M defines an object F in the bounded derived category of G-equivariant coherent sheaves on projective space. We develop a necessary condition for F be...
Published in Journal of Algebraic Combinatorics
We study the Hecke algebra H(q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {H}}({\mathbf {q}})$$\end{document} over an arbitrary field F\documentclass[12p...
Published in Open Mathematics
For the Grothendieck group of a split simple linear algebraic group, the twisted γ-filtration provides a useful tool for constructing torsion elements in -rings of twisted flag varieties. In this paper, we construct a non-trivial torsion element in the γ-ring of a complete flag variety twisted by means of a PGO-torsor. This generalizes the construc...
Published in Indian Journal of Pure and Applied Mathematics
In this paper, we consider the rings over which the class of finitely generated strongly Gorenstein projective modules is closed under extensions (called fs-closed rings). We give a characterization about the Grothendieck groups of the category of the finitely generated strongly Gorenstein projective R-modules and the category of the finitely gener...
Published in Milan Journal of Mathematics
In a recent paper, F. Boca investigates the AF algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathfrak{A}}}$$\end{document} associated with the Farey-Stern-...
Published in Archiv der Mathematik
In this paper we shall determine the multiplicities of simple modules in characteristic 2 in the Sp(4, q)-permutation module on projective 3-space P(3, q), q = 2n.
