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<p>Motivated by M-theory, we define a new type of non-associative algebra involving usual and cubic matrices at the same time. The resulting algebra can be regarded as a two-term truncated <i>L</i><sub><i>∞</i></sub> algebra giving rise to a fundamental identity between the two- and the three-bracket. We provide a simple class of concrete examples of such algebras based on the structure constants of a Lie algebra. Connecting to previous results on higher structures, we generalize the construction of Yang-Mills theories, topological BF theory and generalized IKKT models and point out some appearing issues.</p>

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Non-associative algebras of cubic matrices and their gauge theories

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月1日

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  • Ralph Blumenhagen,
  • Antonia Paraskevopoulou,
  • Thomas Raml

摘要

Motivated by M-theory, we define a new type of non-associative algebra involving usual and cubic matrices at the same time. The resulting algebra can be regarded as a two-term truncated L∞ algebra giving rise to a fundamental identity between the two- and the three-bracket. We provide a simple class of concrete examples of such algebras based on the structure constants of a Lie algebra. Connecting to previous results on higher structures, we generalize the construction of Yang-Mills theories, topological BF theory and generalized IKKT models and point out some appearing issues.