What does this research mean for the field?

The T_{3k+3} family of commutative nonassociative algebras provides a unified mathematical framework characterized by weak power-associativity and O(k+1, 2k+1) automorphism groups, with progressive dimensions corresponding to specific models in supergravity, string theory, and M-theory. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

What question did this study set out to answer?

Formulate and systematically characterize the unified T_{3k+3} family of commutative nonassociative algebras and investigate their physical applications across quantum field theory and string theory.

September 2, 2026Open Access

The Family: A Unified Framework for Nonassociative Algebras From T3 to T21 and Beyond 代数家族 T3

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Authors

ZLZhongqiang Liu

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Overview

Theoretical framework demonstrates unified nonassociative algebraic structures across multidimensional models, suggesting deep connections between gauge field theories and supergravity.

Key Points

Formulate and systematically characterize the unified T_{3k+3} family of commutative nonassociative algebras and investigate their physical applications across quantum field theory and string theory.
Constructed the T_{3k+3} family using a generalized multiplication rule paired with a signature-(k+1, 2k+1) inner product for dimensions ranging from 3 to 21.
Performed detailed theoretical analyses of the T9 member (k=2) via O(3,5) gauge field theory, topological soliton modeling, lattice Monte Carlo quantum simulations, and supersymmetry breaking.
Demonstrated that all family members preserve commutativity, weak power-associativity, an exact Fundamental Theorem of Calculus in mid-point calculus, and an O(k+1, 2k+1) automorphism group.
Derived associator-induced non-perturbative structures in T9, resolving specific topological soliton profiles including kinks, vortices, monopoles, and instantons alongside quantum supersymmetry breaking.
Established progressive structural correspondences connecting higher members (T12, T15, T18, and T21) directly to F-theory, maximal supergravity, and M-theory compactifications.

Cite This Study

Zhongqiang Liu (2026) studied this question.

synapsesocial.com/papers/6a97e2eac562ede874ec75a6 https://doi.org/10.5281/zenodo.22206932

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September 2, 2026Open Access

The Family: A Unified Framework for Nonassociative Algebras From T3 to T21 and Beyond 代数家族 T3

View Full Paper

Ask AI

Bookmark

Authors

ZLZhongqiang Liu

Discussion

Member takes

Overview

Theoretical framework demonstrates unified nonassociative algebraic structures across multidimensional models, suggesting deep connections between gauge field theories and supergravity.

Key Points

Formulate and systematically characterize the unified T_{3k+3} family of commutative nonassociative algebras and investigate their physical applications across quantum field theory and string theory.
Constructed the T_{3k+3} family using a generalized multiplication rule paired with a signature-(k+1, 2k+1) inner product for dimensions ranging from 3 to 21.
Performed detailed theoretical analyses of the T9 member (k=2) via O(3,5) gauge field theory, topological soliton modeling, lattice Monte Carlo quantum simulations, and supersymmetry breaking.
Demonstrated that all family members preserve commutativity, weak power-associativity, an exact Fundamental Theorem of Calculus in mid-point calculus, and an O(k+1, 2k+1) automorphism group.
Derived associator-induced non-perturbative structures in T9, resolving specific topological soliton profiles including kinks, vortices, monopoles, and instantons alongside quantum supersymmetry breaking.
Established progressive structural correspondences connecting higher members (T12, T15, T18, and T21) directly to F-theory, maximal supergravity, and M-theory compactifications.

Cite This Study

Zhongqiang Liu (2026) studied this question.

synapsesocial.com/papers/6a97e2eac562ede874ec75a6 https://doi.org/10.5281/zenodo.22206932

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