1,720,994 research outputs found
NEAR-RINGS AND GROUPS OF AFFINE MAPPINGS
No full textWe classify semi-topological locally compact and semi-algebraic
near-rings R where the set of non-invertible elements of R forms an ideal I
of R such that the multiplicative group of R/I acts sharply transitively on
I\{0}. To achieve our results we use as a main tool the classi cation of
locally compact and algebraic (2; 2)-transformation groups given in two previuos papers
Locally compact (2, 2)-transformation groups
No full textWe determine all locally compact imprimitive transformation groups acting sharply 2-transitively on a non-totally disconnected quotient space of blocks inducing on any block a sharply 2-transitive group and satisfying the following condition: if Δ1, Δ2 are two distinct blocks and Pi, Qi ∈ Δi (i = 1, 2), then there is just one element in the inertia subgroup which maps Pi onto Qi. These groups are natural generalizations of the group of affine mappings of the line over the algebra of dual numbers over the field of real or complex numbers or over the skew-field of quaternions. For imprimitive locally compact groups, our results correspond to the classical results of Kalscheuer for primitive locally compact groups (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Algebraic (2,2)-transformation groups
Get PDFIn this paper we determine all algebraic trans-formation groups G, defined over an algebraical-ly closed field k, which operate transitively, but not primitively, on a variety M, provided the following conditions are fulfilled. We ask that the (non-effective) action of G on the va-riety of blocks is sharply 2-transitive, as well as the action on a block X of the normalizer Gx. Also we require sharp transitivity on pairs (X,Y)of independent points of M, i.e. points con-tained in different blocks
Multiplicative Loops of Quasifields Having Complex Numbers as Kernel
No full textWe determine the multiplicative loops of locally compact connected
4-dimensional quasifields Q having the field of complex numbers
as their kernel. In particular, we turn our attention to multiplicative loops
which have either a normal subloop of dimension one or which contain a
subgroup isomorphic to Spin3(R). Although the 4-dimensional semifields
Q are known, their multiplicative loops have interesting Lie groups generated
by left or right translations. We determine explicitly the quasifields
Q which coordinatize locally compact translation planes of dimension 8
admitting an at least 16-dimensional Lie group as automorphism group
Multiplicative loops of 2-dimensional topological quasifields
No full textWe determine the algebraic structure of the multiplicative loops for locally compact 2-dimensional topological connected quasifields. In particular, our attention turns to multiplicative loops which have either a normal subloop of positive dimension or which contain a 1-dimensional compact subgroup. In the last section, we determine explicitly the quasifields which coordinatize locally compact translation planes of dimension 4 admitting an at least 7-dimensional Lie group as collineation group
Imprimitive groups highly transitive on blocks
Get PDFWe classify imprimitive groups acting highly transitively on blocks and satisfying conditions common in geometry. They can be realized as suitable subgroups of twisted wreath products
Algebraic groups and Lie groups with few factors
No full textAlgebraic groups are treated in this volume from a group theoretical point of view and the obtained results are compared with the analogous issues in the theory of Lie groups. The main body of the text is devoted to a classification of algebraic groups and Lie groups having only few subgroups or few factor groups of different type. In particular, the diversity of the nature of algebraic groups over fields of positive characteristic and over fields of characteristic zero is emphasized. This is revealed by the plethora of three-dimensional unipotent algebraic groups over a perfect field of positive characteristic, as well as, by many concrete examples which cover an area systematically. In the final section, algebraic groups and Lie groups having many closed normal subgroups are determined
A short note on O*-algebras and quantum dynamics
No full textWe review some recent results concerning algebraic dynamics and O*-algebras. We also give a perturbative condition which can be used, in connection with previous results, to define a time evolution via a limiting procedure
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