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An alternative way to classify some Generalized Elliptic Curves and their isotopic loops

Lucien Bénéteau, M. Abou Hashish (2004)

Commentationes Mathematicae Universitatis Carolinae

The Generalized Elliptic Curves ( GECs ) are pairs ( Q , T ) , where T is a family of triples ( x , y , z ) of “points” from the set Q characterized by equalities of the form x . y = z , where the law x . y makes Q into a totally symmetric quasigroup. Isotopic loops arise by setting x * y = u . ( x . y ) . When ( x . y ) . ( a . b ) = ( x . a ) . ( y . b ) , identically ( Q , T ) is an entropic GEC and ( Q , * ) is an abelian group. Similarly, a terentropic GEC may be characterized by x 2 . ( a . b ) = ( x . a ) ( x . b ) and ( Q , * ) is then a Commutative Moufang Loop ( CML ) . If in addition x 2 = x , we have Hall GECs and ( Q , * ) is an exponent 3

An analogue of the Duistermaat-van der Kallen theorem for group algebras

Wenhua Zhao, Roel Willems (2012)

Open Mathematics

Let G be a group, R an integral domain, and V G the R-subspace of the group algebra R[G] consisting of all the elements of R[G] whose coefficient of the identity element 1G of G is equal to zero. Motivated by the Mathieu conjecture [Mathieu O., Some conjectures about invariant theory and their applications, In: Algèbre non Commutative, Groupes Quantiques et Invariants, Reims, June 26–30, 1995, Sémin. Congr., 2, Société Mathématique de France, Paris, 1997, 263–279], the Duistermaat-van der Kallen...

An application of metric diophantine approximation in hyperbolic space to quadratic forms.

Sanju L. Velani (1994)

Publicacions Matemàtiques

For any real τ, a lim sup set WG,y(τ) of τ-(well)-approximable points is defined for discrete groups G acting on the Poincaré model of hyperbolic space. Here y is a 'distinguished point' on the sphere at infinity whose orbit under G corresponds to the rationals (which can be regarded as the orbit of the point at infinity under the modular group) in the classical theory of diophantine approximation.In this paper the Hausdorff dimension of the set WG,y(τ) is determined for geometrically finite groups...

An associative operation on monogenic left distributive systems

Patrick Dehornoy (1995)

Commentationes Mathematicae Universitatis Carolinae

Term substitution induces an associative operation on the free objects of any equational variety. In the case of left distributivity, the construction can be extended to any monogenic structure.

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