Showing papers in "Journal of Algebra in 2007"

TL;DR: In this paper, the relationship between two square-free cycle sets operating transitively on each other was investigated and a Galois theory between ideals of braces and quotient cycle sets was established.

TL;DR: In this article, the problem of weakly s-permutable subgroups in finite groups has been studied under the assumption that all subgroups H with |H | = |D | are weakly S-permutable in G.

TL;DR: In this paper, the classification of 6-dimensional nilpotent Lie algebras over any field of characteristic not 2 is presented. But the proof of this classification is essentially constructive: following the steps of the proof, it is possible to find a Lie algebra M that occurs in the classification, and an isomorphism L → M.

TL;DR: In this paper, the authors prove the uniqueness theorems of graph C ∗ -algebras and give necessary and sufficient conditions for their simplicity, and also give a proof of the fact that for any graph E the Leavitt path algebra L C (E ) embeds as a dense ∗-subalgebra of the graph E ∗ (E).

TL;DR: In this article, the cone of effective divisors and the total coordinate ring of wonderful varieties were studied, and it was shown that the cone can be obtained from that of the associated wonderful variety by a base change of invariant subrings.

TL;DR: In this article, it was shown that if R is any local ring with more than 27 elements, and R is not a field, then Γ ( R ) is not planar.

TL;DR: In this paper, an integral Freudenthal construction relating Jordan algebras and exceptional algebraic groups is proposed, which is related to higher composition laws of M. Bhargava in number theory.

TL;DR: In this paper, a combinatorial approach was proposed to study the minimal free resolutions of edge ideals, that is, quadratic square-free monomial ideals, and recover most of the known results on edge ideals with fuller generality.

TL;DR: In this paper, the authors presented a decomposition of the three-point loop algebra into a direct sum of three subalgebras, each of which is isomorphic to the Onsager algebra.

TL;DR: In this article, it was shown that the invariant algebra S(ge)ge is a graded polynomial algebra in l variables, and this continues to hold for some nilpotent elements in Lie algebras of other types.

TL;DR: In this paper, the authors studied algebraic K3 surfaces with a symplectic automorphism of prime order and showed that the invariant sublattice and its perpendicular complement coincide with the Coxeter-Todd lattice.

TL;DR: In this article, the residual properties of relatively hyperbolic groups were studied and it was shown that if a group G is non-elementary and hyper-bolic relative to a collection of proper subgroups, then G is SQ-universal.

TL;DR: In this article, isolated points in the space of finitely generated groups are investigated and a workable characterization of isolated groups and their hereditary properties are given. But the authors also discuss a connection between isolated points and the solvability of the word problem.

TL;DR: In this paper, the principal minors of a symmetric n × n -matrix form a vector of length 2 n, and they are characterized in terms of algebraic equations derived from the 2 × 2 × n × 2 -hyperdeterminant.

TL;DR: In this article, a complete analysis of finite-dimensional representations of the Lie superalgebra is presented, in particular, the decomposition of all tensor products into their indecomposable building blocks.

TL;DR: In this paper, the authors give a formula, depending only on the structure constants, representing the infinitesimal generators, X i = X i 0 t in g ⊗ k k [ [ [ t ] ], where t is a formal variable, as a formal power series in t with coefficients in the Weyl algebra A n.

TL;DR: In this paper, it has been shown that the zero-divisor graph of a ring R has an even number of edges for any two distinct vertices x and y, x → y is an edge if and only if x y = 0.

TL;DR: In this article, the class of connected graded algebras which are finitely generated in degree 1 was investigated and it was shown that each such algebra is completely characterized by a multilinear form satisfying a twisted cyclicity condition and some other nondegeneracy conditions depending on the global dimension D.

TL;DR: In this article, the authors consider five possible extensions of the Prufer domain notion to the case of commutative rings with zero divisors and relate the corresponding properties on a ring with the property of its total ring of quotients.

TL;DR: In this paper, it was shown that the number of irreducible characters having degree q e is some polynomial in q with integer coefficients (depending on n and e).

TL;DR: In this article, a new version of the Schur-Zassenhaus Theorem in terms of X-semipermutable subgroups is given, and the properties of such subgroups are studied.

TL;DR: In this article, the authors define explicit minimal generators and defining relations for the subring of invariants and show X is a degree 6 hyper-surface in C 9 mapping onto C 8.

TL;DR: In this article, it was shown that a certain orbit category considered by Keller encodes the combinatorics of the m-clusters of Fomin and Reading in a fashion similar to the way the cluster category of Buan, Marsh, Reineke, Reiten, and Todorov encodes combinatoric properties of the clusters of Zelevinsky.

TL;DR: For an Ext-finite abelian category over a commutative noetherian complete local ring, this paper proved that triangulated categories with bounded t -structures are Karoubian.

TL;DR: In this article, a general theorem about the cellularity of twisted semigroup algebras of regular semigroups was proved, which allows us to easily reproduce the cellularness of these algesbras.

TL;DR: The formal cohomology modules of the punctured spectrum SpecR∖V(m) are studied in this paper, where the authors analyze their structure, the upper and lower vanishing and non-vanishing in terms of intrinsic data of M, and its functorial behavior.

TL;DR: In this article, Dettweiler and Reiter give a construction algorithm for differential systems which correspond to rigid local systems on the punctured affine line via the Riemann-Hilbert correspondence.

TL;DR: In this paper, the authors classified all linearly compact simple Jordan superalgebras over an algebraically closed field of characteristic zero and deduced the classification of unital compact unital simple generalized Poisson superalgesbras.

TL;DR: In this paper, the fixed point ratios in actions of finite classical groups are studied. But the main result of this paper is that if G is a finite almost simple classical group and Ω is a faithful transitive non-subspace G -set then either fpr ( x ) ≲ | x G | − 1 2 for all elements x ∈ G of prime order, or ( G, Ω ) is one of a small number of known exceptions.

TL;DR: In this paper, the authors studied quadratic Lie algebras over a field K of null characteristic which admit, at the same time, a symplectic structure and showed that if K is algebraically closed, every such Lie algebra may be constructed as the T ∗ -extension of a nilpotent Lie algebra admitting an invertible derivation and also as the double extension of another quadralatic symplectic Lie algebra by the one-dimensional Lie algebra.