TL;DR
This paper introduces classical and quantum covariant Weil algebras, generalizing Weil and family algebras, with structures like differentials and curvatures, aiming to aid in constructing Mackey's analogue.
Contribution
It presents the first formulation of covariant Weil algebras, extending existing algebraic frameworks with differential and curvature structures.
Findings
Defined differentials, Lie derivatives, and contractions on covariant Weil algebras
Expressed curvatures within these algebras
Proposed potential applications in Mackey's analogue construction
Abstract
In this paper we introduce the classical and quantum covariant Weil algebras. Covariant Weil algebras are simultaneous generalizations of Weil algebras and family algebras. We will define differentials, Lie derivatives and contractions on them to make them curved-dg algebras. Moreover, the expression of curvatures will be given. It is hoped that covariant Weil algebras can be used in the construction of Mackey's analogue.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Nonlinear Waves and Solitons