Algebraic theories of brackets and related (co)homologies
Iosif Krasil'shchik
TL;DR
This paper develops a general algebraic framework for brackets like Frolicher-Nijenhuis and Schouten-Nijenhuis, explores related (co)homologies, and discusses applications in geometry.
Contribution
It introduces a unified algebraic theory of these brackets and their (co)homologies within modules over commutative algebras, extending their geometric applications.
Findings
Unified algebraic framework for brackets and (co)homologies
Discussion of related structures and invariants
Applications to geometric contexts
Abstract
A general theory of the Frolicher-Nijenhuis and Schouten-Nijenhuis brackets in the category of modules over a commutative algebra is described. Some related structures and (co)homology invariants are discussed, as well as applications to geometry.
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