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Spinors in braided geometry

Mićo Đurđević, Zbigniew Oziewicz (1996)

Banach Center Publications

Let V be a ℂ-space, σ ∈ E n d ( V ⊗ 2 ) be a pre-braid operator and let F ∈ l i n ( V ⊗ 2 , ℂ ) . This paper offers a sufficient condition on (σ,F) that there exists a Clifford algebra Cl(V,σ,F) as the Chevalley F-dependent deformation of an exterior algebra C l ( V , σ , 0 ) ≡ V ∧ ( σ ) . If σ ≠ σ - 1 and F is non-degenerate then F is not a σ-morphism in σ-braided monoidal category. A spinor representation as a left Cl(V,σ,F)-module is identified with an exterior algebra over F-isotropic ℂ-subspace of V. We give a sufficient condition on braid σ that the spinor representation...

SPR0 substitutions and families of algebraic Riccati equations

G. Fernández-Anaya, J. C. Martínez García, Vladimír Kučera, D. Aguilar George (2006)

Kybernetika

We study in this paper Algebraic Riccati Equations associated with single-input single-output linear time-invariant systems bounded in H ∞ -norm. Our study is focused in the characterization of families of Algebraic Riccati Equations in terms of strictly positive real (of zero relative degree) substitutions applied to the associated H ∞ -norm bounded system, each substitution characterizing then a particular member of the family. We also consider here Algebraic Riccati Equations associated with systems...

Stabilizers for nondegenerate matrices of boundary format and Steiner bundles.

Carla Dionisi (2004)

Revista Matemática Complutense

In this paper nondegenerate multidimensional matrices of boundary format in V0 ⊗ ... ⊗ Vp are investigated by their link with Steiner vector bundles on product of projective spaces. For any nondegenerate matrix A the stabilizer for the SL(V0) x ... x SL(Vp)-action, Stab(A), is completely described. In particular we prove that there exists an explicit action of SL(2) on V0 ⊗ ... ⊗ Vp such that Stab(A)0 ⊆ SL(2) and the equality holds if and only if A belongs to a unique SL(V0) x ... x SL(Vp)-orbit...

Stable vector bundles over cuspidal cubics

Lesya Bodnarchuk, Yuriy Drozd (2003)

Open Mathematics

We give a complete classification of stable vector bundles over a cuspidal cubic and calculate their cohomologies. The technique of matrix problems is used, similar to [2, 3].

Steiner forms

Jan Hora (2016)

Commentationes Mathematicae Universitatis Carolinae

A trilinear alternating form on dimension n can be defined based on a Steiner triple system of order n . We prove some basic properties of these forms and using the radical polynomial we show that for dimensions up to 15 nonisomorphic Steiner triple systems provide nonequivalent forms over G F ( 2 ) . Finally, we prove that Steiner triple systems of order n with different number of subsystems of order ( n - 1 ) / 2 yield nonequivalent forms over G F ( 2 ) .

Strict spectral approximation of a matrix and some related problems

Krystyna Ziętak (1997)

Applicationes Mathematicae

We show how the strict spectral approximation can be used to obtain characterizations and properties of solutions of some problems in the linear space of matrices. Namely, we deal with (i) approximation problems with singular values preserving functions, (ii) the Moore-Penrose generalized inverse. Some properties of approximation by positive semi-definite matrices are commented.

Strong 𝐗 -robustness of interval max-min matrices

Helena Myšková, Ján Plavka (2021)

Kybernetika

In max-min algebra the standard pair of operations plus and times is replaced by the pair of operations maximum and minimum, respectively. A max-min matrix A is called strongly robust if the orbit x , A ⊗ x , A 2 ⊗ x , ⋯ reaches the greatest eigenvector with any starting vector. We study a special type of the strong robustness called the strong X-robustness, the case that a starting vector is limited by a lower bound vector and an upper bound vector. The equivalent condition for the strong X-robustness is introduced...

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