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1.
In this article,we study the Lie supertriple system(LSTS)T over a field K admitting a nondegenerate invariant supersymmetric bilinear form(call such a T metrisable).We give the definition of T_ω~*-extension of an LSTS T,prove a necessary and sufficient condition for a metrised LSTS(T,φ)to be isometric to a T~*-extension of some LSTS,and determine when two T~*-extensions of an LSTS are"same",i.e.,they are equivalent or isometrically equivalent. 相似文献
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An n-Lie algebra analogue of Schur’s theorem and its converse as well as a Lie algebra analogue of Baer’s theorem and its converse are presented. Also, it is shown that, an n-Lie algebra with finite dimensional derived subalgebra and finitely generated central factor is isoclinic to some finite dimensional n-Lie algebra. 相似文献
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Donald W. BARNES 《数学学报(英文版)》2008,24(1):159-166
Engel subalgebras of finite-dimensional n-Lie algebras are shown to have similar properties to those of Lie algebras. Using these, it is shown that an n-Lie algebra, all of whose maximal subalgebras are ideals, is nilpotent. A primitive 2-soluble n-Lie algebra is shown to split over its minimal ideal, and all the complements to its minimal ideal are conjugate. A subalgebra is shown to be a Cartan subalgebra if and only if it is minimal Engel, provided that the field has sufficiently many elements. Cartan subalgebras are shown to have a property analogous to intravariance. 相似文献
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The Frattini Subalgebra of n-Lie Algebras 总被引:3,自引:0,他引:3
Rui Pu BAI Liang Yun CHEN Dao Ji MENG 《数学学报(英文版)》2007,23(5):847-856
In this paper, we mainly study the structural notions of Frattini subalgebra and Jacobson radical of n-Lie algebras. The properties on Frattini subalgebra and the relationship between the Frattini subalgebra and Jacobson radical are studied. Moreover, we also study them when an n-Lie algebra is strong semi-simple, k-solvable and nilpotent. 相似文献
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Xinhong Chen 《代数通讯》2017,45(2):849-865
For any skewed-gentle algebra, we characterize its indecomposable Gorenstein projective modules explicitly and describe its Cohen–Macaulay Auslander algebra. We prove that skewed-gentle algebras are always Gorenstein, which is independent of the characteristic of the ground field, and the Cohen–Macaulay Auslander algebras of skewed-gentle algebras are also skewed-gentle algebras. 相似文献
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We construct an explicit isomorphism between blocks of cyclotomic Hecke algebras and (sign-modified) cyclotomic Khovanov-Lauda
algebras in type A. These isomorphisms connect the categorification conjecture of Khovanov and Lauda to Ariki’s categorification
theorem. The Khovanov-Lauda algebras are naturally graded, which allows us to exhibit a non-trivial ℤ-grading on blocks of
cyclotomic Hecke algebras, including symmetric groups in positive characteristic. 相似文献
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A. Walendziak 《Periodica Mathematica Hungarica》1991,23(3):219-226
In the present paper we give a common generalization of subdirect product, direct product and weak direct product of given algebras.
Mathematics subject classification numbers, 1980/85 Primary 08A30; Secondary 061310. 相似文献
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The theorem on pseudoanalyticity of continuous functions with constant -extension is proved; this is an analog of the well known results due to Bohr, Rademacher, Men'shov, and Trokhimchuk concerning the analyticity of functions with constant extension.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 4, pp. 459–465, April, 1993. 相似文献
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V. M. Tsvetkov 《Journal of Mathematical Sciences》1999,95(2):2161-2163
It is proved that the rational number field has one, and only one, normal 2-extension (2, t8)/with group isomorphic to
.If is the maximal subfield of a real-closed field, which does not contain
,then the algebraic closure
of is isomorphic to the field
.Bibliography: 7titles.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 236, 1997, pp. 192–196. 相似文献
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Yun-ge XU Yang HAN & Wen-feng JIANG Faculty of Mathematics & Computer Science Hubei University Wuhan China Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2007,50(5):727-736
For a truncated quiver algebra over a field of an arbitrary characteristic, its Hochschild cohomology is calculated. Moreover, it is shown that its Hochschild cohomology algebra is finitedimensional if and only if its global dimension is finite if and only if its quiver has no oriented cycles. 相似文献
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We analyze the extent to which a quantum universal enveloping algebra of a Kac–Moody algebra g is defined by multidegrees of its defining relations. To this end, we consider a class of character Hopf algebras defined by the same number of defining relations of the same degrees as the Kac–Moody algebra g. We demonstrate that if the generalized Cartan matrix A of g is connected then the algebraic structure, up to a finite number of exceptional cases, is defined by just one “continuous” parameter q related to a symmetrization of A, and one “discrete” parameter m related to the modular symmetrizations of A. The Hopf algebra structure is defined by n(n−1)/2 additional “continuous” parameters. We also consider the exceptional cases for Cartan matrices of finite or affine types in more detail, establishing the number of exceptional parameter values in terms of the Fibonacci sequence. 相似文献
17.
A commutative Rota–Baxter algebra can be regarded as a commutative algebra that carries an abstraction of the integral operator. With the motivation of generalizing the study of algebraic geometry to Rota–Baxter algebras, we extend the central concept of localization for commutative algebras to commutative Rota–Baxter algebras. The existence of such a localization is proved and, under mild conditions, its explicit construction is obtained. The existence of tensor products of commutative Rota–Baxter algebras is also proved and the compatibility of localization and the tensor product of Rota–Baxter algebras is established. We further study Rota–Baxter coverings and show that they form a Grothendieck topology. 相似文献
18.
V. T. Filippov 《Siberian Mathematical Journal》1999,40(1):174-184
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