Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
Geometric Means and Reflection Quasigroups
Authors: J. Lawson and Y. Lim
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Abstract
In this paper we show how the category of reflection quasigroups forms a natural and suitable context for the development of an abstract theory of the geometric mean, as it appears in matrix and operator theory. We provide a new characterization of those quasigroups that arise when reflection quasigroups are endowed with the mean operation. We also show how the notion of the geometric mean can be enlarged to that of weighted means, develop basic properties of the latter, and illustrate their usefulness in solving equations involving the mean operation.Jimmie Lawson
Department of Mathematics,
Louisiana State University,
Baton Rouge, LA 70803,
U.S.A.
E-mail:
____________________
Yongdo Lim
Department of Mathematics
Kyungpook National Universit,
Taegu 702-701,
Korea
E-mail:
Department of Mathematics,
Louisiana State University,
Baton Rouge, LA 70803,
U.S.A.
E-mail:
____________________
Yongdo Lim
Department of Mathematics
Kyungpook National Universit,
Taegu 702-701,
Korea
E-mail:
Fulltext
– 0.24 Mb
Contents
- Loop algebras of loops whose derived subloop is central
- Subassociative groupoids
- The construction of loops using right division and Ward quasigroups
- Geometric Means and Reflection Quasigroups
- Ranks of nets
- A short basis for the variety of WIP PACC-loops
- Duality for central piques
- Loops in Relativistic Dynamics
- Evolution algebras
