Showing papers in "Communications in Algebra in 1990"
159 citations
TL;DR: Macpherson's classes of singular algebraic varieties were studied in this article for the first time in the context of algebraic singularity, and they were shown to be monotonically monotone.
Abstract: (1990). Macpherson's chern classes of singular algebraic varieties. Communications in Algebra: Vol. 18, No. 9, pp. 2821-2839.
137 citations
TL;DR: In this paper, the authors revisited the separation of functors in algebra and discussed the relation between separable functors and functors with functors, and with their relation to functors.
Abstract: (1990). Separable functors revisited. Communications in Algebra: Vol. 18, No. 5, pp. 1445-1459.
129 citations
126 citations
TL;DR: In this paper, Degenerations of 6-dimensional nilpotent lie algebras over C are studied and the authors show that they can be expressed as a set of 4-dimensional lie algebraic structures over C.
Abstract: (1990). Degenerations of 6-dimensional nilpotent lie algebras over C. Communications in Algebra: Vol. 18, No. 10, pp. 3493-3505.
115 citations
TL;DR: In this paper, the authors introduce the notions of tilting, cotilting, and serially tilted rings, and show how they can be used in algebraic geometry.
Abstract: (1990). Tilting, cotilting, and serially tilted rings. Communications in Algebra: Vol. 18, No. 5, pp. 1585-1615.
97 citations
TL;DR: A character formula for singly atypical modules of the lie superalgebra sl(m/n) Communications in Algebra: Vol. 18, No. 10, pp. 3453-3480 as discussed by the authors.
Abstract: (1990). A character formula for singly atypical modules of the lie superalgebra sl(m/n) Communications in Algebra: Vol. 18, No. 10, pp. 3453-3480.
94 citations
TL;DR: The problem der Berechnung der Charaktertafel is somit zuruckgefuhrt auf die Bestimmung aller Werte der unipotenten Charaktere der einfachen Gruppen vom Lie-Typ.
Abstract: .Alle endlichen Gruppen vom Lie-Typ besitzen eine ausgezeichnete Menge von irreduziblen komplexen Charakteren, die von Lusztig eingefuhrten unipotenten Charaktere. Diese werden fulr einen vorgegebenen Typ unabhangig vom zugrunde liegenden Korper klassifiziert. Aufgrund der ebenfalls von Lusztig bewiesenen Jordan-Zerlegung der irreduziblen komplexen Charaktere laiit sich die Charaktertafel einer jeden endlichen Gruppe G vom Lie-Typ im wesentlichen zusammenbauen, wenn man die unipotenten Charaktere der halbeinfachen Anteile der Zentralisatoren aller halbeinfachen Elemente in G kennt. Das Problem der Berechnung der Charaktertafel ist somit zuruckgefuhrt auf die Bestimmung aller Werte der unipotenten Charaktere der einfachen Gruppen vom Lie-Typ.
92 citations
TL;DR: In this paper, the r-modular Brauer character of the special unitary groups SU(3, q2) for odd primes r not dividing q is studied.
Abstract: The purpose of this paper is to study the r-modular Brauer character of the special unitary groups SU(3, q2) for odd primes r not dividing q. It turns out that we encounter unexpected difficulties in the principal r-block in the case r‖q + 1. Some ways are described how to attack this problem, which are at least sufficient to solve the problem for an infinite number of prime powers q.
71 citations
TL;DR: In this article, the authors define equiprime near-rings, which are another generalization of primeness in rings, and prove that if a ring is a near-ring and A ⊲ B ⊆ N such that B/A is equip-rime, then A⊲ N is a Kurosh-Amitsur radicial for which holds for all ideals I of N. Moreover, where j 3 is the Jacobson-type radical with equality if N has the descending chain condition on N-subgroups.
Abstract: The usual definition of primeness for near-rings does not lead to a Kurosh-Amitsur radical class for zerosymmetric near-rings (cf. Kaarli and Kriis[5]). In this paper, we define equiprime near-rings, which are another generalization of primeness in rings. Various results are proved, amongst others, for zerosymmetric near-rings:If N is a near-ring and A ⊲ B ⊲ N such that B/A is equiprime, then A ⊲ N. We define . Then p∗ is a Kurosh-Amitsur radicial for which holds for all ideals I of N. Moreover , where j 3 is the Jacobson-type radical which was introduced by Holcombe, with equality if N has the descending chain condition on N-sub-groups.
51 citations
TL;DR: An inversion formula for relative kazhdan polynomials was proposed by as discussed by the authors, which is a polynomial inversion of the LZT formula for polynomorphisms.
Abstract: (1990). An inversion formula for relative kazhdan—lusztig polynomials. Communications in Algebra: Vol. 18, No. 2, pp. 371-387.
TL;DR: In this paper, the authors define the properties that are left invariant under stable equivalence, i.e., properties that cannot be changed under stable equivalence, and show that these properties are not always true.
Abstract: (1990). Properties that are Left Invariant Under Stable Equivalence. Communications in Algebra: Vol. 18, No. 12, pp. 4141-4169.
TL;DR: In this paper, the action of super vertex operators is constructed for a 2l-dimensional C-vector space A. The super vertex operator A V,Z : V→V[[z,z-1]] for each element v of the Fock space V. The most important property of the super vertex operation is the associative law.
Abstract: In this paper, we construct the action of super vertex operators In section 1, we construct a Fock space V for a 2l-dimensional C-vector space A. In physics, V appears as the Fock space of Neveu-Schwarz model of dual poins. See Neveu-Schwarz [5]. In mathematics, V appears as the spin representation space of the affine Lie algebra&ŝ2l. See Frenkel [2] and [3]. In section 2, we define a super vertex operator A V,Z : V→V[[z,z-1]] for each element v of the Fock space V. The most important property of the super vertex operators is the so-called associative law. Using this law, we can see that the coefficients v n : V→V in A v,z span a Lie superalgebra and explicitly write down the Lie superbackets in section 3. It is a huge Lie superalgebra called the vertex operator superalgebra of A.
TL;DR: In this paper, the authors continue their investigation of loops which give rise to alternative loop rings, and describe many properties of this class, including diverse examples of Moufang loops which are united by the fact that they have loop rings which are alternative, and discuss analogues in loop theory of a number of important group theoretic constructions.
Abstract: In this paper, the authors continue their investigation of loops which give rise to alternative loop rings. If the coefficient ring has characteristic 2, these loops turn out to form a surprisingly wide class, in contrast to the situation of characteristic ≠ 2. This paper describes many properties of this class, includes diverse examples of Moufang loops which are united by the fact that they have loop rings which are alternative, and discusses analogues in loop theory of a number of important group theoretic constructions.
TL;DR: In this article, the Groebner ideal generated by all the r × r minors in the generic n × m matrix (Xij) was studied from the point of view of Groebener bases.
Abstract: In this paper we study the well-known example of the ideal generated by all the r × r minors in the generic n × m matrix (Xij) from the point of view of Groebner bases.
TL;DR: In this article, the authors present the Multiplication Modules and Ideals (MMIM) for algebraic algebra. But they do not discuss the relation between multiplication modules and equality.
Abstract: (1990). Multiplication Modules and Ideals. Communications in Algebra: Vol. 18, No. 12, pp. 4353-4375.
TL;DR: In this paper, the cohomology of incidence algebras of partially ordered sets is studied and the authors propose a cohomological model of the partially ordered set of sets.
Abstract: (1990). On the cohomology of incidence algebras of partially ordered sets. Communications in Algebra: Vol. 18, No. 3, pp. 873-887.
TL;DR: In this article, the intrinsic category-theoretic rank for quasitriangular Hopf algebras in the case of the quantum double Hopf algebra of Drinfeld was computed.
Abstract: We compute the intrinsic category-theoretic rank: for quasitriangular Hopf algebras in the case of the quantum double Hopf algebra of Drinfeld. The result is closely related ti recent Hopf algebra invariants of Larson and Radford.
TL;DR: In this paper, it is shown that if the orbit is not (Zariski) closed, then a point in the closure always arises from a deformation. And the role of cohomology is also discussed in deformation and degeneration problems.
Abstract: The purpose of this research-expository paper is to clarify some of the similarities and differences between “orbit closure” and “deformations” . In Section 1 a common formulation for deformation and degeneration is presented. In particular, it is shown that if the orbit is not (Zariski) closed, then a point in the closure always arises from a deformation. In Section 2, the concept of versal deformation is introduced. It is shown that in the case of degeneration there exists a universal element. In Section 3 two definitions of “rigidity” are discussed. It is proved that in the case of Lie algebras over an algebraically closed field of characteristic 0, these two definitions are equivalent. The role of cohomology is also discussed in deformation and degeneration problems.
TL;DR: In this article, it was shown that elementary abelian groups acting quadratically act in weak-closure arguments, pushing-up problems and in problems dealing with parabolic systems.
Abstract: Let G he a finite group and V a faithful, finite dimensional GF 2 G-module. We call E ≤G quadratic,if[V,E,E]=1 and |E|≥4, and we say V is quadratic, if G is generated by its quadratic subgroups. It is an easy exercise, but important for what follows, to show that E has to be elementary abelian. Elementary abelian groups acting quadratically come up quite naturally in weak-closure arguments, pushing-up problems and in problems dealing with parabolic systems. As a successor of [MS] we treat the case that G is a sporadic simple group or an alternating group.
TL;DR: In this article, the q-series of monstrous moonshine and the decomposition of the head characters are discussed, and the authors propose a solution to solve the problem of head decomposition.
Abstract: (1990). The q—-series of monstrous moonshine & the decomposition of the head characters. Communications in Algebra: Vol. 18, No. 1, pp. 253-278.
TL;DR: In this article, the authors represent M11, M12, M22, and M23 on surfaces of least genus, and show how to represent these surfaces in the least genus setting.
Abstract: (1990). Representing M11, M12, M22, and M23 on surfaces of least genus. Communications in Algebra: Vol. 18, No. 1, pp. 15-86.