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Jordan pairs of quadratic forms with values in invertible modules.

Hisatoshi Ikai (2007)

Collectanea Mathematica

Jordan pairs of quadratic forms are generalized so that they have forms with values in invertible modules. The role of such pairs turns out to be natural in describing 'big cells', a kind of open charts around unit sections, of Clifford and orthogonal groups as group schemes. Group germ structures on big cells are particularly interested in and related also to Cayley-Lipschitz transforms.

Semi-groupe de Lie associé à un cône symétrique

Khalid Koufany (1995)

Annales de l'institut Fourier

Soit V une algèbre de Jordan simple euclidienne de dimension finie et Ω le cône symétrique associé. Nous étudions dans cet article le semi-groupe Γ , naturellement associé à V , formé des automorphismes holomorphes du domaine tube T Ω : = V + i Ω qui appliquent le cône Ω dans lui-même.

The group of commutativity preserving maps on strictly upper triangular matrices

Deng Yin Wang, Min Zhu, Jianling Rou (2014)

Czechoslovak Mathematical Journal

Let 𝒩 = N n ( R ) be the algebra of all n × n strictly upper triangular matrices over a unital commutative ring R . A map ϕ on 𝒩 is called preserving commutativity in both directions if x y = y x ϕ ( x ) ϕ ( y ) = ϕ ( y ) ϕ ( x ) . In this paper, we prove that each invertible linear map on 𝒩 preserving commutativity in both directions is exactly a quasi-automorphism of 𝒩 , and a quasi-automorphism of 𝒩 can be decomposed into the product of several standard maps, which extains the main result of Y. Cao, Z. Chen and C. Huang (2002) from fields to rings.

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