K-automorphisms of a weak-crossed product F-algebra over a Galois extension K/F

[摘要] We compute the K-automorphism group of A(K) = K circle times(F) A(f) of a weak crossed product algebra A(f) for a weak 2-cocycle f over a Galois extension K/F with Galois group G. The K-automorphism group of A(K) decomposes into its unipotent part and the reductive part (H) over cap. Automorphisms in (H) over cap are computed via their restriction to semi-simple part of A(K). There is a strong relationship between (H) over cap and the lower-subtractive relation (<=) induced by f on G. We introduce a subgroup of (H) over cap, namely A, which contains interesting combinatorial information of <=. We also present a duality on lower subtractive relations which simplifies the computation of the automorphism group. For the Weak Bruhat order of a Coxeter system, which is an important example of a lower-subtractive relation, it is shown that the automorphism group of the corresponding idempotent algebra is related to the diagram automorphisms of the associated graph. (C) 2019 Elsevier Inc. All rights reserved.

[发布日期] 2019-12-01

[关键词] Weak crossed products;Lower subtractive partial order;Weak Bruhat order