Groups preserving a distributive product are encountered often in algebra. Examples include automorphism groups of associative and nonassociative rings, classical groups, and automorphism groups of p-groups. While the great variety of such products precludes any realistic hope of describing the general structure of the groups that preserve them, it is reasonable to expect that insight may be ga...

This is the first of two articles devoted to a comprehensive exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper is entirely devoted to the study of the tensor-product (infinite-level) limit of fusions rules. We consider thus in detail the problem of constructing tensor-product generating functions in finite Lie algebras. From the be...

We prove explicit formulas for Chern classes of tensor products of vector bundles, with coefficients given by certain universal polynomials in the ranks of the two bundles.

Products were introduced in the 1970s as a natural type of combined modal logics. They arise in different areas of pure and applied logics — spatial reasoning, multi-agent systems, quantified modal and intuitionistic logics etc. The theory of products was systematized and essentially developed first in the paper [GS98] and then in the book [GKWZ03], but during the past 10 years new important re...

The main use of ∗-autonomous categories is in the semantic study of Linear Logic. For this reason, it is thus natural to look for a ∗-autonomous category of locally convex topological vector spaces (tvs). On one hand, Linear Logic inherits its semantics from Linear Algebra, and it is thus natural to build models of Linear Logic from vector spaces [3,5,6,4]. On the other hand, denotational seman...

In this paper we introduce techniques to gauge the torsion of the tensor product A ⊗R B of two finitely generated modules over a Noetherian ring R. The outlook is very different from the study of the rigidity of Tor carried out in the work of Auslander ([1]) and other authors. Here the emphasis in on the search for bounds for the torsion part of A⊗R B in terms of global invariants of A and of B...

We classify all continuous tensor product systems of Hilbert spaces which are “infinitely divisible” in the sense that they have an associated logarithmic structure. These results are applied to the theory of E0-semigroups to deduce that every E0-semigroup possessing sufficiently many “decomposable” operators must be cocycle conjugate to a CCR flow. A path space is an abstraction of the set of ...

It is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies. We look at twisted tensor products, and investigate to which extent this is still true. We give an explicit description of the Ext-algebra of the tensor product of two modules, and under certain additional conditions, describe an essential part of the Hochschild cohomology ring of a t...