B-代数上无穷小双代数的形变
Deformations of Infinitesimal Bialgebras on B-Algebras
DOI: 10.12677/aam.2026.154137, PDF,   
作者: 王晶晶：浙江师范大学数学科学学院，浙江 金华
关键词: B-代数；-算子；无穷小双代数；结合r-矩阵；形变；B-Algebra； -Operators； Infinitesimal Bialgebras； Associative r-Matrix； Deformation
摘要: 本文研究了B-代数上无穷小双代数的形变理论。首先，引入B-代数上无穷小双代数的概念，并说明三角无穷小双代数可以由B-代数上的结合r-矩阵诱导。其次，研究B-代数上无穷小双代数的线性形变，并引入弱同态的概念来刻画形变间的等价关系。最后，证明B-代数上结合r-矩阵的等价形变诱导了无穷小双代数的等价形变。
Abstract: This paper studies the deformation theory of infinitesimal bialgebras on B-algebras. First, we introduce the concept of infinitesimal bialgebras on B-algebras and prove that triangular infinitesimal bialgebras can be induced by associative r-matrices on B-algebras. Second, we study linear deformations and formal deformations of infinitesimal bialgebras on B-algebras, and introduce the notion of weak homomorphisms to characterize the equivalence relation between deformations. Finally, we prove that equivalent deformations of associative r-matrices on B-algebras induce equivalent deformations of infinitesimal bialgebras.
文章引用：王晶晶. B-代数上无穷小双代数的形变[J]. 应用数学进展, 2026, 15(4): 70-77. https://doi.org/10.12677/aam.2026.154137

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