Related papers: Multiary gradings

Multiary gradings

URL: http://arxiv.org/abs/2601.11738v1
Date: Fri, 16 Jan 2026 19:44:27 GMT
Title: Multiary gradings
Authors: Steven Duplij,
Abstract summary: We introduce the notion of grading by multiary groups and investigate various compatibility conditions between the arity of algebra operations and grading group operations.<n>The theory reveals fundamentally new phenomena not present in the binary case, such as the existence of higher power gradings and nontrivial constraints on arity compatibility.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: This article develops a comprehensive theory of multiary graded polyadic algebras, extending the classical concept of group-graded algebras to higher-arity structures. We introduce the notion of grading by multiary groups and investigate various compatibility conditions between the arity of algebra operations and grading group operations. Key results include quantization rules connecting arities, classification of graded homomorphisms, and concrete examples including ternary superalgebras and polynomial algebras over $n$-ary matrices. The theory reveals fundamentally new phenomena not present in the binary case, such as the existence of higher power gradings and nontrivial constraints on arity compatibility.

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