Infinite-dimensional Grassmann-Banach algebras

Details Infinite-dimensional Grassmann-Banach algebras Infinite-dimensional Grassmann-Banach algebras

2000-09-06

arxiv.org/abs/math-ph/0009006v1

Physics

Mathematical Physics

6 pages, Latex

Scientific paper

A short review on infinite-dimensional Grassmann-Banach algebras (IDGBA) is presented. Starting with the simplest IDGBA over $K = {\bf R}$ with $l_1$-norm (suggested by A. Rogers), we define a more general IDGBA over complete normed field $K$ with $l_1$-norm and set of generators of arbitrary power. Any $l_1$-type IDGBA may be obtained by action of Grassmann-Banach functor of projective type on certain $l_1$-space. In non-Archimedean case there exists another possibility for constructing of IDGBA using the Grassmann-Banach functor of injective type.

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