Dipartimento di Matematica, Universita di Bari, 70125 Bari, Italy.
Proc Natl Acad Sci U S A. 1989 Feb;86(3):775-8. doi: 10.1073/pnas.86.3.775.
Let Super(n)[U [unk] V] be the nth homogeneous subspace of the supersymmetric algebra of U [unk] V, where U and V are Z(2)-graded vector spaces over a field K of characteristic zero. The actions of the general linear Lie superalgebras pl(U) and pl(V) span two finite-dimensional K-subalgebras B and [unk] of End(K)(Super(n)[U [unk] V]) that are the centralizers of each other. Young-Capelli symmetrizers and Young-Capelli *-symmetrizers give rise to K-linear bases of B and [unk] containing orthogonal systems of idempotents; thus they yield complete decompositions of B and [unk] into minimal left and right ideals, respectively.
设 Super(n)[U [unk] V] 为 U [unk] V 的超对称代数的第 n 个齐次子空间,其中 U 和 V 是特征为零的域 K 上的 Z(2)-graded 向量空间。一般线性李超代数 pl(U) 和 pl(V) 的作用生成 End(K)(Super(n)[U [unk] V]) 的两个有限维 K-子代数 B 和 [unk],它们是彼此的中心化子。杨-卡皮利对称化子和杨-卡皮利*-对称化子给出了包含正交幂等元系统的 K-线性基 B 和 [unk];因此,它们分别给出了 B 和 [unk] 的完全分解为最小左理想和右理想。