Extensions realising a faithful abstract kernel and their automorphisms

1994 ◽  
Vol 84 (1) ◽  
pp. 135-161 ◽  
Author(s):  
Paul Igodt ◽  
Wim Malfait
Keyword(s):  
Abstract Kernel

scholarly journals On the classification of Schreier extensions of monoids with non-abelian kernel

2020 ◽  
Vol 32 (3) ◽  
pp. 607-623
Author(s):  
Nelson Martins-Ferreira ◽  
Andrea Montoli ◽  
Alex Patchkoria ◽  
Manuela Sobral
Keyword(s):  
Abelian Group ◽  
Cohomology Group ◽  
Isomorphism Classes ◽  
The Third ◽  
Abelian Kernel ◽  
Invertible Elements ◽  
Abstract Kernel

AbstractWe show that any regular (right) Schreier extension of a monoid M by a monoid A induces an abstract kernel {\Phi\colon M\to\frac{\operatorname{End}(A)}{\operatorname{Inn}(A)}}. If an abstract kernel factors through {\frac{\operatorname{SEnd}(A)}{\operatorname{Inn}(A)}}, where {\operatorname{SEnd}(A)} is the monoid of surjective endomorphisms of A, then we associate to it an obstruction, which is an element of the third cohomology group of M with coefficients in the abelian group {U(Z(A))} of invertible elements of the center {Z(A)} of A, on which M acts via Φ. An abstract kernel {\Phi\colon M\to\frac{\operatorname{SEnd}(A)}{\operatorname{Inn}(A)}} (resp. {\Phi\colon M\to\frac{\operatorname{Aut}(A)}{\operatorname{Inn}(A)}}) is induced by a regular weakly homogeneous (resp. homogeneous) Schreier extension of M by A if and only if its obstruction is zero. We also show that the set of isomorphism classes of regular weakly homogeneous (resp. homogeneous) Schreier extensions inducing a given abstract kernel {\Phi\colon M\to\frac{\operatorname{SEnd}(A)}{\operatorname{Inn}(A)}} (resp. {\Phi\colon M\to\frac{\operatorname{Aut}(A)}{\operatorname{Inn}(A)}}), when it is not empty, is in bijection with the second cohomology group of M with coefficients in {U(Z(A))}.

scholarly journals Compactness properties of abstract kernel operators

1982 ◽  
Vol 100 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Charalambos Aliprantis ◽  
Owen Burkinshaw ◽  
M. Duhoux
Keyword(s):  
Kernel Operators ◽  
Abstract Kernel

scholarly journals COMPACT LIE GROUP ACTIONS ON CLOSED MANIFOLDS OF NON-POSITIVE CURVATURE

2006 ◽  
Vol 17 (01) ◽  
pp. 119-127
Author(s):  
BIN XU
Keyword(s):  
Automorphism Group ◽  
Lie Group ◽  
Positive Curvature ◽  
Outer Automorphism ◽  
Harmonic Mappings ◽  
Maximal Dimension ◽  
Natural Homomorphism ◽  
Compact Lie Group ◽  
Aspherical Manifold ◽  
Abstract Kernel

Borel proved that, if a finite group F acts effectively and continuously on a closed aspherical manifold M with centerless fundamental group π1(M), then a natural homomorphism ψ from F to the outer automorphism group Out π1(M) of π1(M), called the associated abstract kernel, is a monomorphism. In this paper, we investigate to what extent Borel's theorem holds for a compact Lie group G acting effectively and smoothly on a particular orientable aspherical manifold N admitting a Riemannian metric g0 of non-positive curvature in case that π1(N) has a non-trivial center. It turns out that if G attains the maximal dimension equal to the rank of Center π1(N) and the metric g0 is real analytic, then any element of G defining a diffemorphism homotopic to the identity of N must be contained in the identity component G0 of G. Moreover, if the inner automorphism group of π1(N) is torsion free, then the associated abstract kernel ψ : G/G0 → Out π1(N) is a monomorphism. The same result holds for the non-orientable N's under certain technical assumptions. Our result is an application of a theorem by Schoen–Yau [12] on harmonic mappings.

scholarly journals The third partial cohomology group and existence of extensions of semilattices of groups by groups

2020 ◽  
Vol 32 (5) ◽  
pp. 1297-1313
Author(s):  
Mikhailo Dokuchaev ◽  
Mykola Khrypchenko ◽  
Mayumi Makuta
Keyword(s):  
Cohomology Group ◽  
The Third ◽  
The Given ◽  
Abstract Kernel

AbstractWe introduce the concept of a partial abstract kernel associated to a group G and a semilattice of groups A and relate the partial cohomology group {H^{3}(G,C(A))} with the obstructions to the existence of admissible extensions of A by G which realize the given abstract kernel. We also show that if such extensions exist, then they are classified by {H^{2}(G,C(A))}.

Performance modeling for GPUs using abstract kernel emulation

2018 ◽  
Vol 53 (1) ◽  
pp. 397-398
Author(s):  
Changwan Hong ◽  
Aravind Sukumaran-Rajam ◽  
Jinsung Kim ◽  
Prashant Singh Rawat ◽  
Sriram Krishnamoorthy ◽  
...  
Keyword(s):  
Performance Modeling ◽  
Abstract Kernel

scholarly journals A non-extendable abstract kernel

2003 ◽  
Vol 47 (1-2) ◽  
pp. 327-328
Author(s):  
L. G. Kovács
Keyword(s):  
Abstract Kernel

scholarly journals GPU code optimization using abstract kernel emulation and sensitivity analysis

2018 ◽  
Vol 53 (4) ◽  
pp. 736-751
Author(s):  
Changwan Hong ◽  
Aravind Sukumaran-Rajam ◽  
Jinsung Kim ◽  
Prashant Singh Rawat ◽  
Sriram Krishnamoorthy ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Code Optimization ◽  
Abstract Kernel

scholarly journals Abstract Kernels and Cohomology

1968 ◽  
Vol 8 (3) ◽  
pp. 544-546
Author(s):  
S. Swierczkowski
Keyword(s):  
Automorphism Group ◽  
Obvious Manner ◽  
Inner Automorphisms ◽  
Abstract Kernel

Let G, N be groups, let A(N) be the automorphism group of N and let I(N) be the subgroup of inner automorphisms. A homomorphism θ: G → A(N)/I(N) will be denoted by (G, N, θ) and called an abstract kernel. (G, N, θ) induces in an obvious manner a structure of a (left) G-module on the centre C of N. A well known construction of Eilenberg and MacLane [1, § 7–9] assigns to (G, N, θ) its obstruction Obs (G, N, θ) ∈H3(G, C). This assignment is such that if C is an arbitrary G-module then every element of H3(G, C) is of the form Obs (G, N, θ) for a suitable abstract kernel (G, N, θ).

Performance modeling for GPUs using abstract kernel emulation

2018 ◽  
Author(s):  
Changwan Hong ◽  
Aravind Sukumaran-Rajam ◽  
Jinsung Kim ◽  
Prashant Singh Rawat ◽  
Sriram Krishnamoorthy ◽  
...  
Keyword(s):  
Performance Modeling ◽  
Abstract Kernel
Sign in / Sign up

Export Citation Format

Share Document