
TL;DR
This paper reviews the construction and properties of Borcherds algebras, especially the Monstrous Lie algebras linked to the Monster group, and explores their applications in string theory and related open problems.
Contribution
It provides an overview of Borcherds algebras, details the construction of Monstrous Lie algebras, and discusses recent developments in associating Lie groups to these algebras.
Findings
Monstrous Lie algebras relate to the Monster group.
Connections to Heterotic String models are discussed.
Open problems in the theory are summarized.
Abstract
We give an overview of the construction of Borcherds algebras, particularly the Monstrous Lie algebras constructed by Carnahan, where is an element of the Monster finite simple group. When is the identity element, is the Monster Lie algebra of Borcherds. We discuss the appearance of the in compactified models of the Heterotic String. We also summarize recent work on associating Lie group analogs to the Lie algebras . We include a discussion of some open problems.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra
