Algebraic exponentiation for Lie algebras

2020/06/12 by Xabier García‐Martínez, García-Martínez, Xabier, James Richard Andrew Gray +1 · 1 citation
Mathematics · #17B99 #18A40 #18D10 #18D15 #18E99 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2006.07077

openalex publication_date 2020/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known that the category of Lie algebras over a ring admits algebraic exponents. The aim of this paper is to show that the same is true for the category of internal Lie algebras in an additive, cocomplete, symmetric, closed, monoidal category. In this way, we add some new examples to the brief list of known locally algebraically cartesian closed categories, including the categories of Lie superalgebras and differentially graded Lie algebras amongst others.

Cited by

• Algebras with representable representations

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