The group of automorphisms of certain subalgebras of matrix algebras

Jøndrup, S.

doi:10.1016/0021-8693(91)90206-n

Cited by 32 publications

(10 citation statements)

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“…Since S is a PID, it is well known that the S-automorphisms of M n (S) are inner; see, for example, [10]. Since all of the Ω j 's are conjugate by [14,Theorem 17.3], every S-automorphism of Ω j is inner for all 1 ≤ j ≤ n. Thus, σ = ι z for some z ∈ (Ω j )…”

Section: Lemma 47 Let U Be the Matrix Defined Asmentioning

confidence: 99%

Hereditary crossed products

Haefner

Janusz

2000

Trans. Amer. Math. Soc.

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Abstract. We characterize when a crossed product order over a maximal order in a central simple algebra by a finite group is hereditary. We need only concentrate on the cases when the group acts as inner automorphisms and when the group acts as outer automorphisms. When the group acts as inner automorphisms, the classical group algebra result holds for crossed products as well; that is, the crossed product is hereditary if and only if the order of the group is a unit in the ring. When the group is acting as outer automorphisms, every crossed product order is hereditary, regardless of whether the order of the group is a unit in the ring.

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Section: Lemma 47 Let U Be the Matrix Defined Asmentioning

confidence: 99%

Hereditary crossed products

Haefner

Janusz

2000

Trans. Amer. Math. Soc.

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“…To determine the automorphisms of classical Lie algebras over commutative rings was recently studied in [1][2][3][4][5][6][7]. In this article, based on the main theorem in [2], we give an explicit description of the automorphisms of the standard Borel subalgebra l of sp(2m, R), provided that R is a commutative ring with identity, 2 is invertible in R.…”

Section: Introductionmentioning

confidence: 98%

Automorphisms of the standard Borel subalgebra of Lie algebra ofC_mtype over a commutative ring

Wang

2007

Linear and Multilinear Algebra

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“…Quite a lot of authors have investigated the automorphisms of triangular matrix algebras [2,9], rings [7] and groups [13,16,22]. (Some more interesting information on this subgroups of unitriangular matrices can be found in [14].…”

Section: Introductionmentioning

confidence: 98%