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61.
We define symmetric spaces in arbitrary dimension and over arbitrary non-discrete topological fields
, and we construct manifolds and symmetric spaces associated to topological continuous quasi-inverse Jordan pairs and -triple systems. This class of spaces, called smooth generalized projective geometries, generalizes the well-known (finite or infinite-dimensional) bounded symmetric domains as well as their ‘compact-like’ duals. An interpretation of such geometries as models of Quantum Mechanics is proposed, and particular attention is paid to geometries that might be considered as ‘standard models’ – they are associated to associative continuous inverse algebras and to Jordan algebras of hermitian elements in such an algebra.Mathematics Subject Classiffications (2000). primary: 17C36, 46H70, 17C65; secondary:
17C30, 17C90 相似文献
62.
We characterize hereditary (as coalgebras) Hopf algebras by the property of ‘equivariant smoothness’, and apply the result
to generalize to the super-context, the category equivalence, due to Hochschild, between the unipotent algebraic affine groups
and the finite-dimensional nilpotent Lie algebras, in characteristic zero. The global dimension of commutative Hopf algebras,
regarded as coalgebras, is also discussed.
Presented by S. Montgomery
Mathematics Subject Classification (2000) 16W30. 相似文献
63.
64.
Daszkiewicz Andrzej Kraśkiewicz Witold Przebinda Tomasz 《Central European Journal of Mathematics》2005,3(3):430-474
We classify the homogeneous nilpotent orbits in certain Lie color algebras and specialize the results to the setting of a
real reductive dual pair.
For any member of a dual pair, we prove the bijectivity of the two Kostant-Sekiguchi maps by straightforward argument. For
a dual pair we determine the correspondence of the real orbits, the correspondence of the complex orbits and explain how these
two relations behave under the Kostant-Sekiguchi maps. In particular we prove that for a dual pair in the stable range there
is a Kostant-Sekiguchi map such that the conjecture formulated in [6] holds. We also show that the conjecture cannot be true
in general. 相似文献
65.
66.
67.
本文研究了泛欧氏空间的Clifford群、扭群、旋群,它们为Clifford代数中选出极好的一类子群.利用Clifford代数理论方法,获得了泛欧氏空间中Clifford群、扭群、旋群及其李代数的结构及它们之间的关系,并且得到了它们的李代数. 相似文献
68.
In this paper we explicitly determine automorphism group of filiform Lie algebra Rn to find the indecomposable solvable Lie algebras with filiform Lie algebra Rn nilradicals.We also prove that the indecomposable solvable Lie algebras with filiform Rn nilradicals is complete. 相似文献
69.
非交换的Poisson代数同时具有(未必交换的)结合代数和李代数两种代数结构,且结合代数和李代数之间满足所谓的Leibniz法则.本文确定了一般广义仿射李代数上所有的Poisson代数结构. 相似文献
70.
《Journal of Pure and Applied Algebra》2023,227(6):107311
The present paper, though inspired by the use of tensor hierarchies in theoretical physics, establishes their mathematical credentials, especially as genetically related to Lie algebra crossed modules. Gauging procedures in supergravity rely on a pairing – the embedding tensor – between a Leibniz algebra and a Lie algebra. Two such algebras, together with their embedding tensor, form a triple called a Lie-Leibniz triple, of which Lie algebra crossed modules are particular cases. This paper is devoted to showing that any Lie-Leibniz triple induces a differential graded Lie algebra – its associated tensor hierarchy – whose restriction to the category of Lie algebra crossed modules is the canonical assignment associating to any Lie algebra crossed module its corresponding unique 2-term differential graded Lie algebra. This shows that Lie-Leibniz triples form natural generalizations of Lie algebra crossed modules and that their associated tensor hierarchies can be considered as some kind of ‘lie-ization’ of the former. We deem the present construction of such tensor hierarchies clearer and more straightforward than previous derivations. We stress that such a construction suggests the existence of further well-defined Leibniz gauge theories. 相似文献