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941.
T. V. Skrypnyk 《Theoretical and Mathematical Physics》2008,155(1):633-645
Using the R-operator on a Lie algebra
satisfying the modified classical Yang-Baxter equation, we define two sets of functions that mutually commute with respect
to the initial Lie-Poisson bracket on
. We consider examples of the Lie algebras
with the Kostant-Adler-Symes and triangular decompositions, their R-operators, and the corresponding two sets of mutually
commuting functions in detail. We answer the question for which R-operators the constructed sets of functions also commute
with respect to the R-bracket. We briefly discuss the Euler-Arnold-type integrable equations for which the constructed commutative
functions constitute the algebra of first integrals.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 1, pp. 147–160, April, 2008. 相似文献
942.
Let k be the algebraic closure of a finite field F_q and A be a finite dimensional k-algebra with a Frobenius morphism F.In the present paper we establish a relation between the stable module category of the repetitive algebra of A and that of the repetitive algebra of the fixed-point algebra A~F.As an application,it is shown that the derived category of A~F is equivalent to the subcategory of F-stable objects in the derived category of A when A has a finite global dimension. 相似文献
943.
Wenhua Zhao 《Journal of Algebraic Combinatorics》2008,28(2):235-260
In this paper, we construct explicitly a noncommutative symmetric (
CS) system over the Grossman-Larson Hopf algebra of labeled rooted trees. By the universal property of the
CS system formed by the generating functions of certain noncommutative symmetric functions, we obtain a specialization of
noncommutative symmetric functions by labeled rooted trees. Taking the graded duals, we also get a graded Hopf algebra homomorphism
from the Connes-Kreimer Hopf algebra of labeled rooted forests to the Hopf algebra of quasi-symmetric functions. A connection
of the coefficients of the third generating function of the constructed
CS system with the order polynomials of rooted trees is also given and proved. 相似文献
944.
In the study of Lie powers of a module V in prime characteristic p, a basic role is played by certain modules B
n
introduced by Bryant and Schocker. The isomorphism types of the B
n
are not fully understood, but these modules fall into infinite families
, one family B(k) for each positive integer k not divisible by p, and there is a recursive formula for the modules within B(k). Here we use combinatorial methods and Witt vectors to show that each module in B(k) is isomorphic to a direct sum of tensor products of direct summands of the kth tensor power V
⊗
k
.
To the memory of Manfred Schocker. 相似文献
945.
946.
We prove the following result concerning the degree spectrum of the atom relation on a computable Boolean algebra. Let be a computable Boolean algebra with infinitely many atoms and be the Turing degree of the atom relation of . If is a c.e. degree such that , then there is a computable copy of where the atom relation has degree . In particular, for every c.e. degree , any computable Boolean algebra with infinitely many atoms has a computable copy where the atom relation has degree .
947.
In this paper we provide a general method to prove that certain nonlinear families of continuous functions contain dense linear manifolds. An application is furnished.
948.
N. A. Koreshkov 《Russian Mathematics (Iz VUZ)》2008,52(12):28-35
We study properties of n-tuple algebras of associative type. We show that the nilpotency of an n-tuple algebra of associative type is determined by the nilpotency of each element. In addition, we characterize the nilpotency of an n-tuple algebra of associative type in terms of the trace function. In the final part of the paper, we show that a homogeneously semisimple n-tuple algebra of associative type is the direct sum of two-sided ideals each of which is a homogeneously simple n-tuple algebra of associative type. 相似文献
949.
Boris Širola 《Algebras and Representation Theory》2008,11(3):233-250
Let \(\mathfrak g\) be a semisimple Lie algebra over a field \(\mathbb K\), \(\text{char}\left( \mathbb{K} \right)=0\), and \(\mathfrak g_1\) a subalgebra reductive in \(\mathfrak g\). Suppose that the restriction of the Killing form B of \(\mathfrak g\) to \(\mathfrak g_1 \times \mathfrak g_1\) is nondegenerate. Consider the following statements: ( 1) For any Cartan subalgebra \(\mathfrak h_1\) of \(\mathfrak g_1\) there is a unique Cartan subalgebra \(\mathfrak h\) of \(\mathfrak g\) containing \(\mathfrak h_1\); ( 2) \(\mathfrak g_1\) is self-normalizing in \(\mathfrak g\); ( 3) The B-orthogonal \(\mathfrak p\) of \(\mathfrak g_1\) in \(\mathfrak g\) is simple as a \(\mathfrak g_1\)-module for the adjoint representation. We give some answers to this natural question: For which pairs \((\mathfrak g,\mathfrak g_1)\) do ( 1), ( 2) or ( 3) hold? We also study how \(\mathfrak p\) in general decomposes as a \(\mathfrak g_1\)-module, and when \(\mathfrak g_1\) is a maximal subalgebra of \(\mathfrak g\). In particular suppose \((\mathfrak g,\sigma )\) is a pair with \(\mathfrak g\) as above and σ its automorphism of order m. Assume that \(\mathbb K\) contains a primitive m-th root of unity. Define \(\mathfrak g_1:=\mathfrak g^{\sigma}\), the fixed point algebra for σ. We prove the following generalization of a well known result for symmetric Lie algebras, i.e., for m=2: (a) \((\mathfrak g,\mathfrak g_1)\) satisfies ( 1); (b) For m prime, \((\mathfrak g,\mathfrak g_1)\) satisfies ( 2). 相似文献
950.
In this paper we discuss the K-groups of Wiener algebra ;W. For the 1-shift space XGM2,We obtain a characterization of Fredholm operators on X^nGM2 for all n ∈ N. We also calculate the K-groups of operator algebra on the 1-shift space XGM2. 相似文献