共查询到20条相似文献,搜索用时 93 毫秒
1.
Carlo Toffalori 《代数通讯》2013,41(1):331-344
ABSTRACT Representations of simple Jordan superalgebras of Hermitian 3?×?3 matrices over the exceptional simple alternative superalgebras B (1,2) and B (4,2) of characteristic 3 are studied. Every irreducible bimodule over these superalgebras up to isomorphism is either a regular bimodule or its opposite. As corollaries,some analogues of the Kronecker factorization theorem are proved for Jordan superalgebras that contain H3(B (1,2)) and H3(B(4,2)). 相似文献
2.
The nucleus of a Malcev superalgebra M measures how far it is from being a Lie superalgebraM being a Lie superalgebra if and only if its nucleus is the whole M. This paper is devoted to study Malcev superalgebras in the opposite direction, that is, with trivial nucleus. The odd part of any finite-dimensional Malcev superalgebra with trivial nucleus is shown to be contained in the solvable radical. For algebraically closed fields, any such superalgebra splits as the sum of its solvable radical and a semisimple Malcev algebra contained in the even part, which is a direct sum of copies of sl(2, F) and the seven-dimensional simple non-Lie Malcev algebra, obtained from the Cayley-Dickson algebra. 相似文献
3.
We describe the simple special unital Jordan superalgebras with associative even part A whose odd part M is an associative module over A. We prove that each of these superalgebras, not isomorphic to a superalgebra of nondegenerate bilinear superform, is isomorphically embedded into a twisted Jordan superalgebra of vector type. We exhibit a new example of a simple special Jordan superalgebra. We also describe the superalgebras such that M [A,M] 0. 相似文献
4.
5.
We study the simple right alternative superalgebras whose even part is trivial; i.e., the even part has zero product. A simple right alternative superalgebra with the trivial even part is singular. The first example of a singular superalgebra was given in [1]. The least dimension of a singular superalgebra is 5. We prove that the singular 5-dimensional superalgebras are isomorphic if and only if suitable quadratic forms are equivalent. In particular, there exists a unique singular 5-dimensional superalgebra up to isomorphism over an algebraically closed field. 相似文献
6.
7.
R. Fallah-Moghaddam 《代数通讯》2017,45(9):3724-3729
Let D be a noncommutative finite dimensional F-central division algebra and M a noncommutative maximal subgroup of GLn(D). It is shown that either M contains a noncyclic free subgroup or M is absolutely irreducible and there exists a unique maximal subfield K of Mn(D) such that K*M, K∕F is Galois with Gal(K∕F)?M∕K* and Gal(K∕F) is a finite simple group. 相似文献
8.
Suppose that V is a finite faithful irreducible G-module where G is a finite solvable group of odd order. We prove if the action is quasi-primitive, then either F(G) is abelian or G has at least 212 regular orbits on V. As an application, we prove that when V is a finite faithful completely reducible G-module for a solvable group G of odd order, then there exists v ∈ V such that C G (v) ? F 2(G) (where F 2(G) is the 2nd ascending Fitting subgroup of G). We also generalize a result of Espuelas and Navarro. Let G be a group of odd order and let H be a Hall π-subgroup of G. Let V be a faithful G-module over a finite field of characteristic 2, then there exists v ∈ V such that C H (v) ? O π(G). 相似文献
9.
Let M be an orientable compact irreducible and ∂-irreducible 3-manifold, and suppose ∂M consists of two boundary components F1 and F2 with g(F1)=g(F2)>1. Let Mf be the closed orientable 3-manifold obtained by identifying F1 and F2 via a homeomorphism f:F1→F2. With the assumption that M is small or g(M,F1)=g(M)+g(F1), we show that if f is sufficiently complicated, then g(Mf)=g(M,∂M)+1. 相似文献
10.
Xu Sheng Liu 《数学学报(英文版)》2010,26(2):361-368
We prove the following vanishing theorem. Let M be an irreducible symmetric space of noncompact type whose dimension exceeds 2 and M ≠SO0(2, 2)/SO(2) × SO(2). Let π : E →* M be any vector bundle. Then any E-valued L2 harmonic 1-form over M vanishes. In particular we get the vanishing theorem for harmonic maps from irreducible symmetric spaces of noncompact type. 相似文献
11.
Let F be a non-Archimedean local field of residual characteristic two and let d be an odd positive integer. Let D be a central F-division algebra of dimension d
2. Let π be one of: an irreducible smooth representation of D
× , an irreducible cuspidal representation of GL
d
(F), an irreducible smooth representation of the Weil group of F of dimension d. We show that, in all these cases, if π is self-contragredient then it is defined over
\mathbb Q{\mathbb Q} and is orthogonal. We also show that such representations exist. 相似文献
12.
Let (K, M, H) be an upper triangular biomodule problem. Brüstle and Hille showed that the opposite algebra A of the endomorphism algebra of a projective generator P of the matrices category of (K, M, H) is quasi-hereditary, and there is an equivalence between the category of Δ-good modules of A and Mat(K, M). In this note, based on the tame theorem for bimodule problems, we show that if the algebra A associated with an upper triangular bimodule problem is of Δ-tame representation type, then the category F(Δ) has the homogeneous property, i.e. almost all modules in F(Δ) are isomorphic to their Auslander-Reiten translations. Moreover, if (K, M, H) is an upper triangular bipartite bimodule problem, then A is of Δ-tame representation type if and only if F(Δ) is homogeneous.
This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 10426014, 10501010 and 19331030)
and the Foundation of Hubei Provincial Department of Education (Grant No. D200510005). 相似文献
13.
In this paper, the authors study a class of generalized intersection matrix Lie algebras gim(Mn), and prove that its every finite-dimensional semisimple quotient is of type M(n, a, c, d). Particularly, any finite dimensional irreducible gim(Mn) module must be an irreducible module of Lie algebra of type M(n, a, c, d) and any finite dimensional irreducible module of Lie algebra of type M(n, a, c, d) must be an irreducible module of gim(Mn). 相似文献
14.
Britta Späth 《Mathematische Zeitschrift》2009,261(3):571-595
Let G be a simply-connected simple algebraic group over an algebraically closed field of characteristic p with a Frobenius map F : G → G and G := G
F
, such that the root system is of exceptional type or G is a Suzuki group or Steinberg’s triality group. We show that all irreducible characters of C
G
(S), the centraliser of S in G, extend to their inertia group in N
G
(S), where S is any F-stable Sylow torus of (G, F). Together with the work in [16] this implies that the McKay conjecture is true for G and odd primes ℓ different from the defining characteristic. Moreover it shows important properties of the associated simple
groups, which are relevant for the proof that the associated simple groups are good in the sense of Isaacs, Malle and Navarro,
as defined in [14].
This research has been supported by the DFG-grant “Die Alperin-McKay-Vermutung für endliche Gruppen” and an Oberwolfach Leibniz
fellowship. 相似文献
15.
Let F be an algebraically closed field of characteristic zero and L an RA loop. We prove that the loop algebra FL is in the variety generated by the split Cayley–Dickson algebra Z F over F. For RA2 loops of type M(Dih(A), ?1,g 0), we prove that the loop algebra is in the variety generated by the algebra 3 which is a noncommutative simple component of the loop algebra of a certain RA2 loop of order 16. The same does not hold for the RA2 loops of type M(G, ?1,g 0), where G is a non-Abelian group of exponent 4 having exactly 2 squares. 相似文献
16.
We describe the simple Lie superalgebras arising from the unital structurable superalgebras of characteristic 0 and construct four series of the unital simple structurable superalgebras of Cartan type. We give a classification of simple structurable superalgebras of Cartan type over an algebraically closed field F of characteristic 0. Together with the Faulkner theorem on the classification of classical such superalgebras, it gives a classification of the simple structurable superalgebras over F. 相似文献
17.
In this paper we determine the irreducible projective representations of sporadic simple groups over an arbitrary algebraically closed field F, whose image contains an almost cyclic matrix of prime-power order. A matrix M is called cyclic if its characteristic and minimum polynomials coincide, and we call M almost cyclic if, for a suitable α ∈F, M is similar to diag(α·Id h , M 1), where M 1 is cyclic and 0 ≤ h ≤ n. The paper also contains results on the generation of sporadic simple groups by minimal sets of conjugate elements. 相似文献
18.
Anton S. Galaev 《Annals of Global Analysis and Geometry》2012,42(1):1-27
Possible irreducible holonomy algebras
\mathfrakg ì \mathfrakosp(p, q|2m){\mathfrak{g}\subset\mathfrak{osp}(p, q|2m)} of Riemannian supermanifolds under the assumption that
\mathfrakg{\mathfrak{g}} is a direct sum of simple Lie superalgebras of classical type and possibly of a 1-dimensional center are classified. This
generalizes the classical result of Marcel Berger about the classification of irreducible holonomy algebras of pseudo-Riemannian
manifolds. 相似文献
19.
Xiaoping Xu 《Frontiers of Mathematics in China》2011,6(4):759-774
Singular vectors of a representation of a finite-dimensional simple Lie algebra are weight vectors in the underlying module
that are nullified by positive root vectors. In this article, we use partial differential equations to explicitly find all
the singular vectors of the polynomial representation of the simple Lie algebra of type F
4 over its 26-dimensional basic irreducible module, which also supplements a proof of the completeness of Brion’s abstractly
described generators. Moreover, we show that the number of irreducible submodules contained in the space of homogeneous harmonic
polynomials with degree k ⩾ 2 is greater than or equal to 〚k/3〛 + 〚(k − 2)/3〛 + 2. 相似文献
20.
Let R be a ring and M a fixed right R-module. A new characterization of M-flatness is given by certain linear equations. For a left R-module F such that the canonical map M? R F → Hom R (M?, F) is injective, where M? = Hom R (M, R), the M-flatness of F is characterized via certain matrix subgroups. An example is given to show that R need not be M-coherent even if every left R-module is M-flat. Moreover, some properties of M-coherent rings are discussed. 相似文献