Showing papers in "Journal of Algebra in 1977"
TL;DR: In this paper, the authors define the Weil representations of general linear groups in Section 1, of symplectic groups (in odd characteristic) in Section 2, of unitary groups for the finite fields, and give the decomposition, the type, and the character of these representations.
244 citations
TL;DR: In this article, the concept of semi-direct product for Hopf algebras has been investigated, and two notions of coadjoint action and smash coproduct have been introduced: the well-known concept of smash product and the dual notion of smash co-product.
179 citations
TL;DR: In this paper, it was shown that Fract( U ( g )/ I ) n is (naturally) isomorphic to the enveloping field of n, and Vergne's geometric version of the Gelfand-Kirillov conjecture is proved for I.
118 citations
TL;DR: In this paper, it was shown that the transitivity of perspectivity on a two-by-two matrix ring over R is additive if and only if R is unit regular.
110 citations
TL;DR: In this article, a simple and effective method for finding all conjugacy classes of G and all orbits of G in Lie Algebra is presented, and the splitting of classes and orbits when G is replaced by a normal subgroup is discussed.
103 citations
77 citations
TL;DR: In this article, the Fortsetzung von Bala-Carter is bewiesen, daβ der Klassifikationssatz of Bala Carter [1, 2] fuðr die nilpotenten Elemente der Lie-Algebra einer halbeinfachen Gruppe in beliebiger guter Charakteristik gilt.
76 citations
TL;DR: In this article, it is shown that a pointed Hopf algebra is free over any Hopf subalgebra (as a left or right module) and that a commutative cocommutative Hopf algebra is also free over Hopf subsalgebras.
69 citations
68 citations
66 citations
TL;DR: In this paper, it was shown that for any group G a topology on G called the verbal topology of G and study groups which satisfy the minimal condition on the closed sets in the topology, called min-cbsed, are C&groups.
TL;DR: Theorem 1.10 as discussed by the authors shows that every projective extension A of R is not a symmetric algebra of an R-module, but is a projective R-algebra.
TL;DR: In this article, the authors assume that d is a topos (in the sense of Lawvere and Tierney, see [9] or [27], though readers unfamiliar with this notion of topos may substitute that of Grothendieck topos without serious damage).
TL;DR: In this paper, all isometries of the algebra of n -square complex matrices which preserve this norm are determined for κ = 1 and κ > n. The result is also related to earlier work of Morita and Russo, respectively.
TL;DR: In this article, it was shown that for the case R = OF-, R, is graded by the nonnegative integers N, R, = K, and P = m, where m = @YE, Ri is the irrelevant maximal ideal.
TL;DR: In this article, the structure of one-dimensional F-pure rings was studied and it was shown that F-purity plays an important role in the invariant theory under the action of reductive algebraic groups.