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Research Paper#Mathematics, Algebra, Group Theory🔬 ResearchAnalyzed: Jan 3, 2026 06:35

Guide to 2-Generated Axial Algebras of Monster Type

Published:Dec 31, 2025 17:33
1 min read
ArXiv

Analysis

This paper provides a detailed analysis of 2-generated axial algebras of Monster type, which are fundamental building blocks for understanding the Griess algebra and the Monster group. It's significant because it clarifies the properties of these algebras, including their ideals, quotients, subalgebras, and isomorphisms, offering new bases and computational tools for further research. This work contributes to a deeper understanding of non-associative algebras and their connection to the Monster group.
Reference

“The paper details the properties of each of the twelve infinite families of examples, describing their ideals and quotients, subalgebras and idempotents in all characteristics. It also describes all exceptional isomorphisms between them.”

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Research Paper#Linear Algebra, Matrix Theory🔬 ResearchAnalyzed: Jan 3, 2026 15:42

New Algorithms for Sign k-Potent Sign Patterns

Published:Dec 30, 2025 14:38
1 min read
ArXiv

Analysis

This paper addresses the construction and properties of sign k-potent sign patterns, which are matrices with entries from {+, -, 0} that satisfy a specific power relationship. It improves upon existing algorithms for constructing these patterns, particularly sign idempotent patterns (k=1), by providing a new algorithm that terminates in a single iteration. The paper also provides an algorithm for constructing sign k-potent patterns and conditions for them to allow k-potence. This is important because it provides more efficient and accurate methods for analyzing and constructing these specific types of matrices, which have applications in various fields.
Reference

“The paper gives a new algorithm that terminates in a single iteration to construct all possible sign idempotent sign patterns.”

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