We study fusion rings for degenerate minimal models (p = q case) for N = 0 and N = 1 (super)conformal algebras. We consider a distinguished family of modules at the level c = 1 and c = 3 2 and show that the corresponding fusion rings are isomorphic to the representation rings for sl(2, C) and osp(1|2) respectively.

A λ-ring is, roughly speaking, a commutative ring R with unit together with operations λi, i ≥ 0, on it that act like the exterior power operations. It is widely used in algebraic topology, algebra, and representation theory. For example, the complex representation ring R(G) of a group G is a λ-ring, where λi is induced by the map that sends a representation to its ith exterior power. Another e...

A commutative associative algebra A over C with a derivation is one of the simplest examples of a vertex algebra. However, the differences between the modules for A as a vertex algebra and the modules for A as an associative algebra are not well understood. In this paper, I give the classification of finite-dimensional indecomposable untwisted or twisted modules for the polynomial ring in one v...

Let G be the linear algebraic group SL3 over a field k of characteristic two. Let A be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. We show that the full cohomology ring H∗(G, A) is finitely generated. This extends the finite generation property of the ring of invariants AG. We discuss where the problem stands for other geometrically reductiv...

Let G be the linear algebraic group SL3 over a field k of characteristic two. Let A be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. We show that the full cohomology ring H(G,A) is finitely generated. This extends the finite generation property of the ring of invariants AG. We discuss where the problem stands for other geometrically reductive ...

We construct chain maps between the bar and Koszul resolutions for a quantum symmetric algebra (skew polynomial ring). This construction uses a recursive technique involving explicit formulae for contracting homotopies. We use these chain maps to compute the Gerstenhaber bracket, obtaining a quantum version of the Schouten-Nijenhuis bracket on a symmetric algebra (polynomial ring). We compute b...

Introduction Let B = k[x 1 ,. .. , x n ] be a polynomial ring over a field k and A = B/J a quotient ring of B by a homogeneous ideal J. Let m denote the maximal graded ideal of A. Then the Rees algebra R = A[mt] may be considered a standard graded k-algebra and has a presentation B[y 1 ,. In this paper we want to compare the ideals J and I J as well as their homological properties.

This is the first of two interconnected parts: Part I contains the geometric theory of generalized modular forms and their connections with the cooperation algebra for elliptic cohomology, E``∗E``, while Part II is devoted to the more algebraic theory associated with Hecke algebras and stable operations in elliptic cohomology. We investigate the structure of the stable operation algebra E``∗E``...

In this paper we investigate a ring of delay-differential operators, which appears in the study of time-delay systems with commensurate point-delays. Besides point-delay differential operators, this ring contains also certain distributed delays. It can be described as a certain algebraic extension of the ring of point-delay differential operators as well as a convolution algebra of compact supp...

We consider the class of algebras of rank 4 equipped with a standard involution over an arbitrary base ring. In particular, we characterize quaternion rings, those algebras defined by the construction of the even Clifford algebra. A quaternion algebra is a central simple algebra of dimension 4 over a field F . Generalizations of the notion of quaternion algebra to other commutative base rings R...