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991.
In a recent article with Oleg Smirnov, we defined short Peirce (SP) graded Kantor pairs. For any such pair P, we defined a family, parameterized by the Weyl group of type BC2, consisting of SP-graded Kantor pairs called Weyl images of P. In this article, we classify finite dimensional simple SP-graded Kantor pairs over an algebraically closed field of characteristic 0 in terms of marked Dynkin diagrams, and we show how to compute Weyl images using these diagrams. The theory is particularly attractive for close-to-Jordan Kantor pairs (which are variations of Freudenthal triple systems), and we construct the reflections of such pairs (with nontrivial gradings) starting from Jordan pairs of matrices. 相似文献
992.
993.
994.
Murray Bremner 《代数通讯》2013,41(4):2131-2145
A triple system is partially associative (by definition) if it satisfies the identity (abc)de + a(bcd)e + ab(cde) ≡ 0. This paper presents a computational study of the free partially associative triple system on one generator with coefficients in the ring Z of integers. In particular, the Z-module structure of the homogeneous submodules of (odd) degrees ≤ 11 is determined, together with explicit generators for the free and torsion components in degrees ≤ 9. Elements of additive order 2 exist in degrees ≥ 7, and elements of additive order 6 exist in degrees ≥ 9. The most difficult case (degree 11) requires finding the row-reduced form over Z of a matrix of size 364 × 273. These computations were done with Maple V.4 on a Sun workstation. 相似文献
995.
996.
We consider random walks in random environments on Zd. Under a transitivity hypothesis that is much weaker than the customary ellipticity condition, and assuming an absolutely continuous invariant measure on the space of the environments, we prove the ergodicity of the annealed process w.r.t. the dynamics “from the point of view of the particle”. This implies in particular that the environment viewed from the particle is ergodic. As an example of application of this result, we give a general form of the quenched Invariance Principle for walks in doubly stochastic environments with zero local drift (martingale condition). 相似文献
997.
For any real division algebra A of finite dimension greater than one, the signs of the determinants of left multiplication and right multiplication by an element a ∈ A?{0} are shown to form an invariant of A, called its double sign. For each n ∈ {2, 4, 8}, the double sign causes the category $\mathbb {D}_nFor any real division algebra A of finite dimension greater than one, the signs of the determinants of left multiplication and right multiplication by an element a ∈ A?{0} are shown to form an invariant of A, called its double sign. For each n ∈ {2, 4, 8}, the double sign causes the category $\mathbb {D}_n$ of all n‐dimensional real division algebras to decompose into four blocks. The structures of these blocks are closely related, and their relationship is made precise for a sample of full subcategories of $\mathscr {D}_n$. 相似文献
998.
Rychkov defined weighted Besov spaces and weighted Triebel‐Lizorkin spaces coming with a weight in the class $A_p^{\rm loc}$, which is even wider than the class Ap due to Muckenhoupt. In the present paper we are concerned with the atomic decomposition of these spaces. As an application, we obtain some key theorems in the theory of function spaces. Finally we conclude this paper with some helpful examples showing the difference between weighted spaces and unweighted spaces. 相似文献
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1000.
We define the notions of trace, determinant and, more generally, Berezinian of matrices over a (Z2)n-graded commutative associative algebra A. The applications include a new approach to the classical theory of matrices with coefficients in a Clifford algebra, in particular of quaternionic matrices. In a special case, we recover the classical Dieudonné determinant of quaternionic matrices, but in general our quaternionic determinant is different. We show that the graded determinant of purely even (Z2)n-graded matrices of degree 0 is polynomial in its entries. In the case of the algebra A=H of quaternions, we calculate the formula for the Berezinian in terms of a product of quasiminors in the sense of Gelfand, Retakh, and Wilson. The graded trace is related to the graded Berezinian (and determinant) by a (Z2)n-graded version of Liouville’s formula. 相似文献