We consider the diffeological version of the Clifford algebra of a (diffeological) finite-dimensional vector space; we start by commenting on the notion of a diffeological algebra (which is the expected analogue of the usual one) and that of a diffeological module (also an expected counterpart of the usual notion). After considering the natural diffeology of the Clifford algebra, and its expected properties, we turn to our main interest, which is constructing pseudo-bundles of diffeological Clifford algebras and those of diffeological Clifford modules, by means of the procedure called diffeological gluing. The paper has a significant expository portion, regarding mostly diffeological algebras and diffeological vector pseudo-bundles. (This paper extends the previous paper by title "Diffeological Clifford algebras" and renders the latter obsolete).

Diffeological Clifford algebras and pseudo-bundles of Clifford modules

PERVOVA, EKATERINA
2019-01-01

Abstract

We consider the diffeological version of the Clifford algebra of a (diffeological) finite-dimensional vector space; we start by commenting on the notion of a diffeological algebra (which is the expected analogue of the usual one) and that of a diffeological module (also an expected counterpart of the usual notion). After considering the natural diffeology of the Clifford algebra, and its expected properties, we turn to our main interest, which is constructing pseudo-bundles of diffeological Clifford algebras and those of diffeological Clifford modules, by means of the procedure called diffeological gluing. The paper has a significant expository portion, regarding mostly diffeological algebras and diffeological vector pseudo-bundles. (This paper extends the previous paper by title "Diffeological Clifford algebras" and renders the latter obsolete).
2019
Pervova, Ekaterina
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/764762
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