We prove that cellular Noetherian algebras with finite global dimension are split quasi-hereditary over a regular commutative ring Krull and their structure is unique, up to equivalence. In the process, we establish algebra semi-perfect if only ground local ring. give formula determine of (with dimension) in terms finite-dimensional algebras. For general case, upper bounds for finitistic arbitr...

Given a group G and an integer n ≥ 2 we construct a new group e K(G, n). Although this construction naturally occurs in the context of finding new invariants for complex algebraic surfaces, it is related to the theory of central extensions and the Schur multiplier. A surprising application is that Abelian groups of odd order possess naturally defined covers that can be computed from a given cov...

A circulant is a Cayley digraph over a finite cyclic group. The classification of arc-transitive circulants is shown. The result follows from earlier descriptions of Schur rings over cyclic groups.

In applications of Weyl character formula for AN Lie algebras, it can be shown that the followings are valid by the use of some properly chosen system of weights which we call fundamental weights. Characters can be attributed conveniently to Weyl orbits rather than representations. The classsical Schur function SN (x1, x2, .., xN ) of degree N can be defined to be character of the representatio...

We determine the Grothendieck rings of category finite-dimensional modules over Queer Lie superalgebras via their characters. In particular, we show that Q ...