Algebraic Structure Analysis of Skew Brauer Graph Algebras Based on Taylor Series Rings

This paper conducts an extensive and in-depth study of the algebraic structure of skew Brauer graph algebras. As a significant extension of Brauer graph algebras, skew Brauer graph algebras exhibit intricate similarities with Taylor series rings, particularly in their generation relations, representations, and underlying algebraic frameworks. By leveraging a comprehensive understanding of Taylor series rings, we analyze the fundamental properties, complex algebraic structures, and multifaceted applications in the representation theory of skew Brauer graph algebras. The paper incorporates a substantial number of mathematical formulas, theorems, and proofs to thoroughly elucidate the algebraic structures and their complexities.