On the graded quotients of the algebra of SL(2) characters of free groups

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The graded quotient of the algebra of SL(2) characters of free groups is invariant under the action of the automorphism group of the free group. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

Y Katoh

doi:10.1515/jgth-2025-0154

February 12, 2026Journal of Group Theory

On the graded quotients of the algebra of SL(2) characters of free groups

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Key Points

To examine the structure of the graded quotient of SL(2) characters associated with free groups.
Analyzed SL(2) characters in the context of free groups of rank n.
Investigated the action of the automorphism group on the algebra of SL(2) characters.
Focused on the augmentation ideal generated by SL(2) characters.
Identified that the augmentation ideal is Aut(F_n)-invariant.
Described the structure of the graded quotient, revealing properties of SL(2) characters under group actions.

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Studies the structure of graded quotients in free groups, implying new insights into representation theory.

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Y Katoh (2026) studied this question.

synapsesocial.com/papers/6992b4469b75e639e9b0930c https://doi.org/10.1515/jgth-2025-0154

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On the graded quotients of the algebra of SL(2) characters of free groups

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On the graded quotients of the algebra of SL(2) characters of free groups

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