All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 15 Next

Displaying 281 – 300 of 914

Showing per page

Invertibility criterion of composition of two multiary quasigroups

Fedir M. Sokhatsky, Iryna V. Fryz (2012)

Commentationes Mathematicae Universitatis Carolinae

We study invertibility of operations that are composition of two operations of arbitrary arities. We find the criterion for quasigroups and specifications for T -quasigroups. For this purpose we introduce notions of perpendicularity of operations and hypercubes. They differ from the previously introduced notions of orthogonality of operations and hypercubes [Belyavskaya G., Mullen G.L.: Orthogonal hypercubes and n -ary operations, Quasigroups Related Systems 13 (2005), no. 1, 73–86]. We establish...

Jordan- and Lie geometries

Wolfgang Bertram (2013)

Archivum Mathematicum

In these lecture notes we report on research aiming at understanding the relation beween algebras and geometries, by focusing on the classes of Jordan algebraic and of associative structures and comparing them with Lie structures. The geometric object sought for, called a generalized projective, resp. an associative geometry, can be seen as a combination of the structure of a symmetric space, resp. of a Lie group, with the one of a projective geometry. The text is designed for readers having basic...

Kikkawa loops and homogeneous loops

Michihiko Kikkawa (2004)

Commentationes Mathematicae Universitatis Carolinae

In H. Kiechle's publication ``Theory of K-loops'' [3], the name Kikkawa loops is given to symmetric loops introduced by the author in 1973. This concept started from an analogical imagination of sum of vectors in Euclidean space brought up on a sphere. In 1975, this concept was extended by him to the more general concept of homogeneous loops, and it led us to a non-associative generalization of the theory of Lie groups. In this article, the backstage of finding these concepts will be disclosed from...

Left MQQs whose left parastrophe is also quadratic

Simona Samardjiska, Danilo Gligoroski (2012)

Commentationes Mathematicae Universitatis Carolinae

A left quasigroup ( Q , q ) of order 2 w that can be represented as a vector of Boolean functions of degree 2 is called a left multivariate quadratic quasigroup (LMQQ). For a given LMQQ there exists a left parastrophe operation q ∖ defined by: q ∖ ( u , v ) = w ⇔ q ( u , w ) = v that also defines a left multivariate quasigroup. However, in general, ( Q , q ∖ ) is not quadratic. Even more, representing it in a symbolic form may require exponential time and space. In this work we investigate the problem of finding a subclass of LMQQs whose left parastrophe...

Left-Garside categories, self-distributivity, and braids

Patrick Dehornoy (2009)

Annales mathématiques Blaise Pascal

In connection with the emerging theory of Garside categories, we develop the notions of a left-Garside category and of a locally left-Garside monoid. In this framework, the relationship between the self-distributivity law LD and braids amounts to the result that a certain category associated with LD is a left-Garside category, which projects onto the standard Garside category of braids. This approach leads to a realistic program for establishing the Embedding Conjecture of [Dehornoy, Braids and...

Lexicographic product decompositions of half linearly ordered loops

Milan Demko (2007)

Czechoslovak Mathematical Journal

In this paper we prove for an hl-loop Q an assertion analogous to the result of Jakubík concerning lexicographic products of half linearly ordered groups. We found conditions under which any two lexicographic product decompositions of an hl-loop Q with a finite number of lexicographic factors have isomorphic refinements.

Currently displaying 281 – 300 of 914