involutorial anti automorphism
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对合反自同构
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Moreover, some subgroups of Aut are obtained, such asthe inner automorphism group, the central automorphism group, the involutional automorphism group, the first and the second extremal automorphism group.
证明了:当n=0时,Aut中每个元素都是内自同构,且Aut≌C(定理1.12)。n=1时,Aut中每个元素都是有限个内自同构,中心自同构,对合自同构和第一类外自同构的乘积(定理1.13)。
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In chapter 5, local derivations and local automorphisms of nest subalgebras in von Neumann algebras and local higher cohomology -local 2-cocycles are studied. It is proved that every weakly continuous local derivation, respectively, every weakly local automorphism, of nest subalgebra of a factor von Neumann algebra is a derivation, respectively, an automorphism. Every norm continuous local derivation, respectively, every norm local automorphism, of the nest subalgebra associated to a countable nest in a factor von Neumann algebra is a derivation, respectively, an automorphism. Moreover, it is answered Larson's question. Finally, it is shown that every local 2-cocycle of any von Neumann algebra is a 2-cocycle.
第五章研究von Neumann代数中套子代数的局部导子和局部同构以及von Neumann代数的高维局部映射—局部2-上循环,证明了因子von Neumann代数中套子代数的每一个局部强连续导子和局部强连续同构分别是导子和同构;可数套所对应的套子代数的每一个有界局部导子和有界局部同构分别是导子和同构;同时,部分回答了Larson所提的问题;最后,得到von Neumann代数的每一个局部2-上循环是2-上循环。
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involutorial anti automorphism:对合反自同构
involution 对合 | involutorial anti automorphism 对合反自同构 | involutory algebra 对合代数