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February 8, 2026Journal of Algebra and Its Applications

Quasi-triangular, factorizable anti-symmetric covariant bialgebras and symmetric Rota-Baxter Frobenius algebras

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Authors

YXYuxiang Xiao

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Overview

Demonstrates the construction of anti-symmetric covariant bialgebras in associative algebras, suggesting new algebra structures.

Key Points

  • The aim is to introduce and explore anti-symmetric covariant bialgebras and establish their relationship with symmetric Rota-Baxter algebras.
  • Introduced anti-symmetric covariant bialgebras as a generalization of balanced infinitesimal bialgebras.
  • Investigated the construction using associative Yang-Baxter pairs under certain symmetry conditions.
  • Developed a factorization theory for factorizable ASC bialgebras.
  • Established a correspondence between symmetric Rota-Baxter Frobenius algebras and factorizable ASC bialgebras.
  • Presented an algorithm for computing associative Yang-Baxter pairs in finite-dimensional algebras.
  • Demonstrated that certain conditions yield a quasi-triangular ASC bialgebra.
  • Established that factorizable ASC bialgebras induce a factorization of their associative algebra.
  • Provided examples of factorizable ASC bialgebras constructed from Rota-Baxter systems.
  • Classified all associative Yang-Baxter pairs in two-dimensional complex associative algebras.

Cite This Study

Yuxiang Xiao (2026) studied this question.

synapsesocial.com/papers/6988292d0fc35cd7a884941dhttps://doi.org/10.1142/s0219498827501532
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