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341.
342.
We deal with iterative algebras of functions of
-valued logic lacking projections, which we call algebras without projections. It is shown that a partially ordered set of algebras of functions of
-valued logic, for
, without projections contains an interval isomorphic to the lattice of all iterative algebras of functions of
-valued logic. It is found out that every algebra without projections is contained in some maximal algebra without projections, which is the stabilizer of a semigroup of non-surjective transformations of the basic set. It is proved that the stabilizer of a semigroup of all monotone non-surjective transformations of a linearly ordered 3-element set is not a maximal algebra without projections, but the stabilizer of a semigroup of all transformations preserving an arbitrary non one-element subset of the basic set is. 相似文献
343.
Under certain constraints on the characteristic of a field , the commutative standard enveloping q-algebra >B of a commutative triple system A over is defined. It is proved that(1) if the algebra B is simple, then the system A is simple;(2) if the system A is simple, then B either is simple or decomposes into the direct sum of two isomorphic simple subalgebras (as of ideals). 相似文献
344.
The highly excited vibrational states of asymmetric linear tetratomic molecules are studied in the framework of Lie algebra.
By using symmetric groupU
1(4)U
2(4)⊗U
3(4), we construct the Hamiltonian that includes not only Casimir operators but also Majorana operators M12, M13 and M23, which are useful for getting potential energy surface and force constants in Lie algebra method. By Lie algebra treatment,
we obtain the eigenvalues of the Hamiltonian, and make the concrete calculation for molecule C2HF. 相似文献
345.
In this paper we give a realization of crystal bases for quantumaffine algebras using some new combinatorial objects which wecall the Young walls. The Young walls consist of colored blockswith various shapes that are built on a given ground-state walland can be viewed as generalizations of Young diagrams. Therules for building Young walls and the action of Kashiwara operatorsare given explicitly in terms of combinatorics of Young walls.The crystal graph of a basic representation is characterizedas the set of all reduced proper Young walls. The characterof a basic representation can be computed easily by countingthe number of colored blocks that have been added to the ground-statewall. 2000 Mathematical Subject Classification: 17B37, 17B65,81R50, 82B23. 相似文献
346.
Dunkl Operators for Complex Reflection Groups 总被引:3,自引:0,他引:3
Dunkl operators for complex reflection groups are defined inthis paper. These commuting operators give rise to a parameterizedfamily of deformations of the polynomial De Rham complex. Thisleads to the study of the polynomial ring as a module over therational Cherednik algebra, and a natural contravariantform on this module. In the case of the imprimitive complexreflection groups G(m, p, N), the set of singular parametersin the parameterized family of these structures is describedexplicitly, using the theory of non-symmetric Jack polynomials.2000 Mathematical Subject Classification: 20F55 (primary), 52C35,05E05, 33C08 (secondary). 相似文献
347.
Structure of Degenerate Block Algebras 总被引:13,自引:0,他引:13
Given a non-trivial torsion-free abelian group (A,+,Q), a field F of characteristic 0, and a non-degenerate bi-additive skew-symmetric map
: A
A
F, we define a Lie algebra
=
(A,
) over F with basis {ex | x
A/{0}} and Lie product [ex,ey] =
(x,y)ex+y. We show that
is endowed uniquely with a non-degenerate symmetric invariant bilinear form and the derivation algebra Der
of
is a complete Lie algebra. We describe the double extension D(
, T) of
by T, where T is spanned by the locally finite derivations of
, and determine the second cohomology group H2(D(
, T),F) using anti-derivations related to the form on D(
, T). Finally, we compute the second Leibniz cohomology groups HL2(
, F) and HL2(D(
, T), F).2000 Mathematics Subject Classification: 17B05, 17B30This work was supported by the NNSF of China (19971044), the Doctoral Programme Foundation of Institution of Higher Education (97005511), and the Foundation of Jiangsu Educational Committee. 相似文献
348.
O. V. Shvartsman 《Functional Analysis and Its Applications》2003,37(2):147-154
We find all pairs (,a) consisting of a cocompact Fuchsian group of genus zero and an automorphy factor a of for which the graded algebra of a--automorphic forms is free. 相似文献
349.
We introduce the notion of the
-prolongation of Lie algebras of differential operators on homogeneous spaces. The
-prolongations are topological invariants that coincide with one-dimensional cohomologies of the corresponding Lie algebras in the case where V is a homogeneous space. We apply the obtained results to the spaces S
1 (the Virasoro algebra) and
. 相似文献
350.
By using hyperbolic virtual unit of Clifford algebra, the concept of n-dimensional space-time unit spheres is introduced. It is used as n-dimensional Minkowski space-time and Lorentz transformation. 相似文献