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arXiv · 1805.09541

Weak Algebra Bundles and Associator Varieties

Clarisson Rizzie Canlubo
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Abstract

Algebra bundles, in the strict sense, appear in many areas of geometry and physics. However, the structure of an algebra is flexible enough to vary non-trivially over a connected base, giving rise to a structure of a weak algebra bundle. We will show that the notion of a weak algebra bundle is more natural than that of a strict algebra bundle. We will give necessary and sufficient conditions for weak algebra bundles to be locally trivial. The collection of non-trivial associative algebras of a fixed dimension forms a projective variety, called associator varieties. We will show that these varieties play the role the Grassmannians play for principal $O(n)$-bundles.

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Clarisson Rizzie Canlubo. 2018-05-24. Weak Algebra Bundles and Associator Varieties. https://arxiv.org/abs/1805.09541

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