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Abstract  

We construct loops which are semidirect products of groups of affinities. As their elements in many cases one may take transversal subspaces of an affine space. In particular we obtain in this manner smooth loops having Lie groups of affine real transformations as the groups generated by left translations, whereas the groups generated by right translations are smooth groups of infinite dimension. We also determine the Akivis algebras of these loops.

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Abstract  

A notion of Gaussian hemigroup is introduced and its relationship with the Gauss condition is studied. Moreover, a Lvy-type martingale characterization is proved for processes with independent (not necessarily stationary) increments satisfying the Gauss condition in a compact Lie group. The characterization is given in terms of a faithful finite dimensional representation of the group and its tensor square. For the proofs noncommutative Fourier theory is applied for the convolution hemigroups associated with the increment processes.

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Differentiable Manifolds and Lie Groups Springer NY . [6] Rham de , G. 1955 Variétés Differentiables

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Acta Mathematica Hungarica
Authors:
Jesús M. Cabezas
,
Luisa M. Camacho
,
José R. Gómez
, and
Bakhrom A. Omirov

Comm. Algebra 29 4197 – 4210 10.1081/AGB-100105996 . [8] Feigin , B. L. , Fuks , D. B. 1988 Cohomology of Lie groups and Lie algebras Itogi Nauki Tekh. Ser. Sovrem. Probl. Mat. Fundam

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, A. Richardson , R. W. Jr. 1967 Deformations of homomorphisms of Lie groups and Lie algebras Bull. Amer. Math. Soc. 73 175 – 179 10.1090/S

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] Jiang , R. J ., Jiang , X. J . and Yang , D. C . , Maximal function characterizations of Hardy spaces associated with Schrödinger operators on nilpotent Lie groups , Rev. Mat. Complut ., 24 ( 2011 ), 251 – 275 . [26] Li , H. Q

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. Some embeddings of Lie groups in Euclidean space . Mathematika , 18 : 152 – 156 , 1971 . [34] D . Repovš and

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,913 −122 22 Topological Groups, Lie Groups 1,301 1,228 875 73 26 Real Functions

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second half of the 20th Century, 13 disciplines were represented in mathematics. These are: the foundations of mathematical logic and mathematics, algebra and number theory, geometry, topology, Lie groups and representation theory, analysis and functional

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like ‘Lie group’, ‘nilpotent group’, ‘locally compact group’, etc. Within the field of algebra, however, the term ‘group’ is practically specific enough to identify a topic. The most obvious approach to label or to represent clusters and topics

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