It is proved that the Wedderburn Theorem on finite division rings implies that all knots and links in the smooth four-dimensional manifolds are trivial.
Communicated by Igor Klep
We consider finite dimensional Jordan superalgebras J over an algebraically closed field of characteristic 0, with solvable radical N such that N=20 and J/N is a simple Jordan superalgebra of one of ...the following types: Kac K10, Kaplansky K3, superform or Dt.
We prove that an analogue of the Wedderburn Principal Theorem (WPT) holds if certain restrictions on the types of irreducible subbimodules of N are imposed, where N is considered as a J/N-bimodule. Using counterexamples, it is shown that the imposed restrictions are essential.
Adequate subgroups and indecomposable modules Guralnick, Robert; Herzig, Florian; Tiep, Pham
Journal of the European Mathematical Society : JEMS,
01/2017, Letnik:
19, Številka:
4
Journal Article
Recenzirano
Odprti dostop
The notion of adequate subgroups was introduced by Jack Thorne 60. It is a weakening of the notion of big subgroups used by Wiles and Taylor in proving automorphy lifting theorems for certain Galois ...representations. Using this idea, Thorne was able to strengthen many automorphy lifting theorems. It was shown in 22 and 23 that if the dimension is smaller than the characteristic then almost all absolutely irreducible representations are adequate. We extend the results by considering all absolutely irreducible modules in characteristic p of dimension p. This relies on a modified definition of adequacy, provided by Thorne in 61, which allows p to divide the dimension of the module. We prove adequacy for almost all irreducible representations of SL$_2 (p^a)$ in the natural characteristic and for finite groups of Lie type as long as the field of definition is sufficiently large. We also essentially classify indecomposable modules in characteristic p of dimension less than $2p-2$ and answer a question of Serre concerning complete reducibility of subgroups in classical groups of low dimension.
We study Γ-conformal algebras which are a discrete analog of conformal algebras in the sense of V. G. Kac. For a torsion-free group Γ, simple and semisimple associative Γ- conformal algebras of ...finite type are described and an analog of Wedderburn’s theorem is proved.
This paper analyzes rank modification of symmetric positive definite matrices H of the form H- M+ P, where H- M denotes a step of reducing H to a lower-rank, symmetric and positive semidefinite ...matrix and ( H- M)+ P denotes a step of restoring H- M to a symmetric positive definite matrix. These steps and their generalizations for rectangular matrices are fully characterized. The well-known BFGS and DFP updates used in Hessian and inverse Hessian approximations provided the motivation for the generalizations and are special cases with H and P having rank one. PUBLICATION ABSTRACT
Celotno besedilo
Dostopno za:
CEKLJ, DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
Let $G \rightarrow GL (V)$ be a faithful orthogonal representation of a finite group $G$ acting in an Euclidean space $V$. For a unit vector $x$ we choose $g \neq 1$ in $G$ so that $| gx - x|$ is ...minimal and put $\delta(x) = |gx - x|. We study the class of vectors $x$ which maximize $\delta(x)$ and have the additional property that $| gx - x|$ depends only on the conjugacy class of $g \in G$. For some special types of representations we are able to characterize completely this class of vectors.
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