Displaying 2141 – 2160 of 2599

Showing per page

Tensor complexes: multilinear free resolutions constructed from higher tensors

Christine Berkesch Zamaere, Daniel Erman, Manoj Kummini, Steven V. Sam (2013)

Journal of the European Mathematical Society

The most fundamental complexes of free modules over a commutative ring are the Koszul complex, which is constructed from a vector (i.e., a 1-tensor), and the Eagon-Northcott and Buchsbaum-Rim complexes, which are constructed from a matrix (i.e., a 2-tensor). The subject of this paper is a multilinear analogue of these complexes, which we construct from an arbitrary higher tensor. Our construction provides detailed new examples of minimal free resolutions, as well as a unifying view on a wide variety...

Tensor products of hermitian lattices

Renaud Coulangeon (2000)

Acta Arithmetica

1. Introduction. The properties of euclidean lattices with respect to tensor product have been studied in a series of papers by Kitaoka ([K, Chapter 7], [K1]). A rather natural problem which was investigated there, among others, was the determination of the short vectors in the tensor product L οtimes M of two euclidean lattices L and M. It was shown for instance that up to dimension 43 these short vectors are split, as one might hope. The present paper deals with a similar question...

The algebra of the subspace semigroup of M ( q )

Jan Okniński (2002)

Colloquium Mathematicae

The semigroup S = S ( M ( q ) ) of subspaces of the algebra M ( q ) of 2 × 2 matrices over a finite field q is studied. The ideal structure of S, the regular -classes of S and the structure of the complex semigroup algebra ℂ[S] are described.

The Brauer category and invariant theory

Gustav I. Lehrer, R. B. Zhang (2015)

Journal of the European Mathematical Society

A category of Brauer diagrams, analogous to Turaev’s tangle category, is introduced, a presentation of the category is given, and full tensor functors are constructed from this category to the category of tensor representations of the orthogonal group O ( V ) or the symplectic group Sp ( V ) over any field of characteristic zero. The first and second fundamental theorems of invariant theory for these classical groups are generalised to the category theoretic setting. The major outcome is that we obtain presentations...

Currently displaying 2141 – 2160 of 2599