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1.
The Terwilliger algebra of a distance-regular graph of negative type
Štefko Miklavič, 2009, original scientific article

Abstract: Let ▫$\Gamma$▫ denote a distance-regular graph with diameter ▫$D \ge 3$▫. Assume ▫$\Gamma$▫ has classical parameters ▫$(D,b,\alpha,\beta)▫$ with ▫$b < -1$▫. Let ▫$X$▫ denote the vertex set of ▫$\Gamma$▫ and let ▫$A \in {\mathrm{Mat}}_X(\mathbb{C})$▫ denote the adjacency matrix of ▫$\Gamma$▫. Fix ▫$x \in X$▫ and let $A^\ast \in {\mathrm{Mat}}_X(\mathbb{C})$ denote the corresponding dual adjacency matrix. Let ▫$T$▫ denote the subalgebra of ${\mathrm{Mat}}_X(\mathbb{C})$ generated by ▫$A,A^\ast$▫. We call ▫$T$▫ the Terwilliger algebra of ▫$\Gamma$▫ with respect to ▫$x$▫. We show that up to isomorphism there exist exactly two irreducible ▫$T$▫-modules with endpoint 1; their dimensions are ▫$D$▫ and ▫$2D-2$▫. For these ▫$T$▫-modules we display a basis consisting of eigenvectors for ▫$A^\ast$▫, and for each basis we give the action of ▫$A$▫.
Found in: ključnih besedah
Summary of found: Zadetek v naslovu
Keywords: distance-regular graph, negative type, Terwilliger algebra
Published: 15.10.2013; Views: 1660; Downloads: 75
URL Full text (0,00 KB)

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Hartwig, Brian: Three mutually adjacent Leonard pairs. (English). - [J] Linear Algebra Appl. 408, 19-39 (2005). [ISSN 0024-3795]
Bojan Kuzma, 2006, review, book review, critique

Found in: ključnih besedah
Summary of found: Zadetek v naslovu
Keywords: matematika, linearna algebra, linearne transformacije, Leonardov par
Published: 15.10.2013; Views: 1829; Downloads: 9
URL Full text (0,00 KB)

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The Hyers-Ulam-Rassias stability of (m,n)[sub]{([sigma], [tau])}-derivations on normed algebras
Ajda Fošner, 2012, original scientific article

Abstract: We study the Hyers-Ulam-Rassias stability of ▫$(m,n)_{(\sigma,\tau)}$▫-derivations on normed algebras.
Found in: ključnih besedah
Summary of found: ...Hyers-Ulam-Rassias stability, normed algebra, ▫$(m,n)_{(\sigma,\tau)}$▫-derivation...
Keywords: Hyers-Ulam-Rassias stability, normed algebra, ▫$(m, n)_{(\sigma, \tau)}$▫-derivation
Published: 15.10.2013; Views: 1247; Downloads: 15
URL Full text (0,00 KB)

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Rank-permutable additive mappings
Anna A. Alieva, Aleksandr Èmilevič Guterman, Bojan Kuzma, 2006, original scientific article

Abstract: Let ▫$\sigma$▫ be a fixed non-identical permutation on ▫$k$▫ elements. Additive bijections ▫$T$▫ on the matrix algebra ▫$M_n(\mathbb{F})$▫ over a field ▫$\mathbb{F}$▫ of characteristic zero, with the property that ▫$\rm{rk} (A_1...A_k) = \rm{rk} (A_{\sigma(1)}...A_{\sigma(k)})$▫ implies the same condition on the ▫$T$▫ images, are characterized. It is also shown that the surjectivity assumption can be relaxed, if this property is preserved in both directions.
Found in: ključnih besedah
Summary of found: ...elements. Additive bijections ▫$T$▫ on the matrix algebra ▫$M_n(\mathbb{F})$▫ over a field ▫$\mathbb{F}$▫ of characteristic...
Keywords: mathematics, linearna algebra, matrix algebra, rank, permutation, additive preservers
Published: 15.10.2013; Views: 1423; Downloads: 51
URL Full text (0,00 KB)

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Nekaj rezultatov v teoriji superalgeber
Maja Fošner, Ajda Fošner, 2011, scientific monograph

Found in: ključnih besedah
Summary of found: ...matematika, algebra, ...
Keywords: matematika, algebra
Published: 15.10.2013; Views: 1853; Downloads: 26
URL Full text (0,00 KB)
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Fosner, Ajda; Šemrl, Peter: Additive maps on matrix algebras preserving invertibility. (English). - [J] Acta Math. Sin., Engl. Ser. 21, No. 4, 681-684 (2005). [ISSN 1439-8516; ISSN 1439-7617]
Bojan Kuzma, 2006, review, book review, critique

Found in: ključnih besedah
Summary of found: ...matematika, linearna algebra, aditivna preslikava, ohranjevalec obrnljivosti, ohranjevalec singularnosti, mat...
Keywords: matematika, linearna algebra, aditivna preslikava, ohranjevalec obrnljivosti, ohranjevalec singularnosti, matrična algebra
Published: 15.10.2013; Views: 1261; Downloads: 19
URL Full text (0,00 KB)

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