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The local integration of Leibniz algebras

Simon Covez (2013)

Annales de l’institut Fourier

This article gives a local answer to the coquecigrue problem for Leibniz algebras, that is, the problem of finding a generalization of the (Lie) group structure such that Leibniz algebras are the corresponding tangent algebra structure. Using links between Leibniz algebra cohomology and Lie rack cohomology, we generalize the integration of a Lie algebra into a Lie group by proving that every Leibniz algebra is isomorphic to the tangent Leibniz algebra of a local Lie rack. This article ends with...

The minimal extension of sequences III. On problem 16 of Grätzer and Kisielewicz

J. Dudek (1996)

Colloquium Mathematicae

The main result of this paper is a description of totally commutative idempotent groupoids. In particular, we show that if an idempotent groupoid (G,·) has precisely m ≥ 2 distinct essentially binary polynomials and they are all commutative, then G contains a subgroupoid isomorphic to the groupoid N m described below. In [2], this fact was proved for m = 2.

The operation A B A in operator algebras

Marcell Gaál (2020)

Commentationes Mathematicae Universitatis Carolinae

The binary operation a b a , called Jordan triple product, and its variants (such as e.g. the sequential product a b a or the inverted Jordan triple product a b - 1 a ) appear in several branches of operator theory and matrix analysis. In this paper we briefly survey some analytic and algebraic properties of these operations, and investigate their intimate connection to Thompson type isometries in different operator algebras.

The table of characters of some quasigroups

Grzegorz Bińczak, Joanna Kaleta (2007)

Discussiones Mathematicae - General Algebra and Applications

It is known that (ℤₙ,-ₙ) are examples of entropic quasigroups which are not groups. In this paper we describe the table of characters for quasigroups (ℤₙ,-ₙ).

The theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry

Oğuzhan Demirel (2009)

Commentationes Mathematicae Universitatis Carolinae

In [Comput. Math. Appl. 41 (2001), 135--147], A. A. Ungar employs the Möbius gyrovector spaces for the introduction of the hyperbolic trigonometry. This Ungar's work plays a major role in translating some theorems from Euclidean geometry to corresponding theorems in hyperbolic geometry. In this paper we explore the theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry.

The upper triangular algebra loop of degree 4

Kenneth Walter Johnson, M. Munywoki, Jonathan D. H. Smith (2014)

Commentationes Mathematicae Universitatis Carolinae

A natural loop structure is defined on the set U 4 of unimodular upper-triangular matrices over a given field. Inner mappings of the loop are computed. It is shown that the loop is non-associative and nilpotent, of class 3. A detailed listing of the loop conjugacy classes is presented. In particular, one of the loop conjugacy classes is shown to be properly contained in a superclass of the corresponding algebra group.

Tolerances on poset algebras

Bohdan Zelinka (1992)

Mathematica Bohemica

To everz partiallz ordered set a certain groupoid is assigned. A tolerance on it is defined similarlz as a congruence, onlz the requirement of transitivitz is omitted. Some theorems concerning these tolerances are proved.

Towards a geometric theory for left loops

Karla Baez (2014)

Commentationes Mathematicae Universitatis Carolinae

In [Mwambene E., Multiples of left loops and vertex-transitive graphs, Cent. Eur. J. Math. 3 (2005), no. 2, 254–250] it was proved that every vertex-transitive graph is the Cayley graph of a left loop with respect to a quasi-associative Cayley set. We use this result to show that Cayley graphs of left loops with respect to such sets have some properties in common with Cayley graphs of groups which can be used to study a geometric theory for left loops in analogy to that for groups.

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