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<p>For an infinite cochain bicomplex, we show that the orthogonality and grading conditions provide it with the structure of a bigraded differential algebra with respect to a natural multiplication of several elements bicomplex spaces. Corresponding bigraded algebra commutation relations generate a sequence of non-vanishing cohomology invariants associated with vertex algebras. In particular, we apply this result to the bicomplex of grading-restricted vertex algebra cohomology endowed with a multiplication we introduce. We provide examples associated with various choices of vertex algebra bicomplex subspaces. The generators and commutation relations of the bigraded differential algebra form a continual Lie algebra with the root space provided by a grading-restricted vertex algebra.</p>

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BIGRADED DIFFERENTIAL ALGEBRA FOR VERTEX ALGEBRA COMPLEXES

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月20日

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  • A. Zuevsky

摘要

For an infinite cochain bicomplex, we show that the orthogonality and grading conditions provide it with the structure of a bigraded differential algebra with respect to a natural multiplication of several elements bicomplex spaces. Corresponding bigraded algebra commutation relations generate a sequence of non-vanishing cohomology invariants associated with vertex algebras. In particular, we apply this result to the bicomplex of grading-restricted vertex algebra cohomology endowed with a multiplication we introduce. We provide examples associated with various choices of vertex algebra bicomplex subspaces. The generators and commutation relations of the bigraded differential algebra form a continual Lie algebra with the root space provided by a grading-restricted vertex algebra.