2019/12/05 by Zheng-Yao Su, Su, Zheng-Yao, Ming-Chung Tsai +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1912.03362
openalex publication_date 2019/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Else from the quotient algebra partition considered in the preceding episodes, two kinds of partitions on unitary Lie algebras are created by nonabelian bi-subalgebras. It is of interest that there exists a partition duality between the two kinds of partitions. With an application of an appropriate coset rule, the two partitions return to a quotient algebra partition when the generating bi-subalgebra is abelian. Procedures are proposed to merge or detach a co-quotient algebra, which help deliver type-AIII Cartan decompositions of more varieties. In addition, every Cartan decomposition is obtainable from the quotient algebra partition of the highest rank. Of significance is the universality of the quotient algebra partition to classical and exceptional Lie algebras.