For Bol loops and reductive loops one can construct an infinitesimal theory similar to Lie group theory by associating with a loop a certain binary-ternary algebra with identities, namely the Bol algebra for a Bol loop and the triple Lie algebra for a reductive loop. It is also possible to construct a proper infinitesimal theory for hyporeductive loops that generalize Bol loops and reductive loops. This can be achieved by associating with these loops a hyporeductive algebra with two binary and one ternary operation and the system of identities [see L. V. Sabinin, in {it Variational methods in modern geometry (Russian)}, 50--69, Univ. Druzhby Narodov, Moscow, 1990; [msn] MR1130903 (92g:22008) [/msn]; Dokl. Akad. Nauk SSSR {bf 314} (1990), no.~3, 565--568; [msn] MR1094021 (92d:22002) [/msn]; in {it Webs and quasigroups (Moscow, 1989)}, 129--137, Tver. Gos. Univ., Tverʹ, 1991; see [msn] MR1140959 (92f:53003) [/msn]]. The latter algebra generalizes both the Bol algebra and the triple Lie algebra. In the paper under review the author constructs the infinitesimal theory for smooth hyporeductive and pseudoreductive loops.

Authors

Sabinin L.V.

Editors

Goldberg Vladislav

Journal

Number of issue

1

Language

English

Pages

1-24

Status

Published

Number

13

Volume

13

Year

1996

Date of creation

19.05.2021

Date of change

19.05.2021

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IZVESTIYA VYSSHIKH UCHEBNYKH ZAVEDENII FIZIKA / Russian Physics Journal.
Издательство научно-технической литературы.
1996.

Communications in Theoretical Physics (Allahabad).
Vol. 2.
1993.
P. 19-37