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921.
922.
R. Fehlberg Jr. 《代数通讯》2013,41(6):2501-2512
Makar–Limanov's conjecture states that, if a division ring D is finitely generated and infinite dimensional over its center k, then D contains a free k-subalgebra of rank 2. In this work, we will investigate the existence of such structures in D, the division ring of fractions of the skew polynomial ring L[t; σ], where t is a variable and σ is a k-automorphism of L. For instance, we prove Makar-Limanov's conjecture when either L is the function field of an abelian variety or the function field of the n-dimensional projective space. 相似文献
923.
We study Lie brackets and Jordan products derived from associative operations ○, ? satisfying the interchange identity (w?x) ○ (y?z) ≡ (w ○ y)?(x ○ z). We use computational linear algebra, based on the representation theory of the symmetric group, to determine all polynomial identities of degree ≤7 relating (i) the two Lie brackets, (ii) one Lie bracket and one Jordan product, and (iii) the two Jordan products. For the Lie–Lie case, there are two new identities in degree 6 and another two in degree 7. For the Lie–Jordan case, there are no new identities in degree ≤6 and a complex set of new identities in degree 7. For the Jordan–Jordan case, there is one new identity in degree 4, two in degree 5, and complex sets of new identities in degrees 6 and 7. 相似文献
924.
Jerry M. Lodder 《代数通讯》2013,41(11):4874-4891
We prove that varieties are uniquely determined by the derived category of 𝒪[[?]]-modules with coherent cohomology which is the same as 𝒪-modules proved by A. Bondal and D. Orlov. We also generalize a theorem of Orlov. 相似文献
925.
Meena Jagadeesan 《代数通讯》2013,41(11):4945-4972
The Möbius polynomial is an invariant of ranked posets, closely related to the Möbius function. In this paper, we study the Möbius polynomial of face posets of convex polytopes. We present formulas for computing the Möbius polynomial of the face poset of a pyramid or a prism over an existing polytope, or of the gluing of two or more polytopes in terms of the Möbius polynomials of the original polytopes. We also present general formulas for calculating Möbius polynomials of face posets of simplicial polytopes and of Eulerian posets in terms of their f-vectors and some additional constraints. 相似文献
926.
In this paper, the authors study a class of generalized intersection matrix Lie algebras gim(Mn), and prove that its every finite-dimensional semisimple quotient is of type M(n, a, c, d). Particularly, any finite dimensional irreducible gim(Mn) module must be an irreducible module of Lie algebra of type M(n, a, c, d) and any finite dimensional irreducible module of Lie algebra of type M(n, a, c, d) must be an irreducible module of gim(Mn). 相似文献
927.
Let SVir be the well-known super-Virasoro algebras. In this paper, we first prove that any super-skewsymmetric super-biderivation of SVir is inner. Based on this, we show that every linear super-commuting map ψ on SVir is of the form ψ(x) = f(x)c, where f is a linear function from SVir to ? mapping the odd part of SVir to zero, and c is the central charge of SVir. 相似文献
928.
In this paper, the concepts of approximate character amenability (contractibility), uniform approximate character amenability (contractibility) and w^*-approximate character amenability are introduced. We are concerned with the relations among the generalized concepts of character amenability for Banach algebras. We show that approximate character amenability, w^*-approximate character amenability and approximate character contractibility are the same properties, as uniform approximate character amenability and character amenability as uniform approximate character contractibility and character contractibility. The general theory for these concepts is also developed. Moreover, approximate character amenability of several concrete classes of Banach algebras related to locally compact groups and also some discrete semigroups is considered. 相似文献
929.
John S. Kauta 《代数通讯》2013,41(11):3566-3589
A nonassociative quaternion algebra over a field F is a 4-dimensional F-algebra A whose nucleus is a separable quadratic extension field of F. We define the notion of a valuation ring for A, and we also define a value function on A with values from a totally ordered group. We determine the structure of the set on which the function assumes non-negative values and we prove that, given a valuation ring of A, there is a value function associated to it if and only if the valuation ring is integral and invariant under proper F-automorphisms of A. 相似文献
930.
Angela Antonou 《代数通讯》2013,41(6):2516-2523
We classify commutative standard table algebras (STA) with at most one nontrivial multiplicity. The main result shows that there exists exactly one nontrivial multiplicity if and only if the table basis is the wreath product of a two-dimensional subalgebra and an abelian group. The theorem applies to adjacency algebras of commutative association schemes with exactly one primitive idempotent matrix of rank greater than one. A theorem of Seitz that characterizes finite groups with exactly one irreducible representation of degree greater than one is another corollary of the main theorem. 相似文献