相关论文: Moufang symmetry II. Moufang-Mal'tsev pairs and tr…
Triple closure of the infinitesimal translations of an analytic Moufang loop is inquired. This property is equivalent to reductivity and relates Mal'tsev algebras to the Lie triple systems.
The continuous Moufang loops are characterized as the algebraic systems where the associativity law is perturbed minimally. The minimal perturbation of associativity is characterized by the first- order partial differential equations, which…
The differential equations for a continuous birepresentation of a local analytic Moufang loop are established. The commutation relations for the infinitesimal operators of the representation are found. These commutation relations can be…
Using groups with triality we obtain some general multiplication formulas in Moufang loops, construct Moufang extensions of abelian groups, and describe the structure of minimal extensions for finite simple Moufang loops over abelian…
Generalized Lie-Cartan theorem for linear birepresentations of an analytic Moufang loop is considered. The commutation relations of the generators of the birepresentation were found. In particular, the Lie algebra of the multiplication…
It is shown how integrability of the generalized Lie equations of a local analytic Moufang loop is related to the reductivity conditions and Sagle-Yamaguti identity.
Nonassociative finite simple Moufang loops are exactly the loops constructed by Paige from Zorn vector matrix algebras. We prove this result anew, using geometric loop theory. In order to make the paper accessible to a broader audience, we…
We give an interpretation of the construction of torsors from preceding work (Bertram, Kinyon: Associative Geometries. I, J. Lie Theory 20) in terms of classical projective geometry. For the Desarguesian case, this leads to a reformulation…
Reductivity in the Ma'tsev algebras is inquired. This property relates the Mal'tsev algebras to the general Lie triple systems.
The present paper investigates a natural generalization of the duality between Riemannian symmetric pairs of compact type and those of non-compact type \`a la \'E. Cartan. The main result of this paper is to construct an explicit…
In this paper, we present some geometric characterizations of the Moufang quadrangles of mixed type, i.e., the Moufang quadrangles all the points and lines of which are regular. Roughly, we classify generalized quadrangles with enough (to…
We use groups with triality to construct a series of nonassociative Moufang loops. Certain members of this series contain an abelian normal subloop with the corresponding quotient being a cyclic group. In particular, we give a new series of…
It is explicitly shown how the Lie algebras can be associated with the analytic Moufang loops. The resulting Lie algebra commutation relations are well known from the theory of alternative algebras and can be seen as a preliminary step to…
Two constructions due to Dr\'apal produce a group by modifying exactly one quarter of the Cayley table of another group. We present these constructions in a compact way, and generalize them to Moufang loops, using loop extensions. Both…
It is shown how integrability of the generalized Lie equations of continous Moufang transformatiosn is related to the reductivity conditions and Sagle-Yamaguti identity.
All known Moufang sets arise, in some way or another, from an algebraic structure which can be called `division' in some way. In this PhD dissertation, I made an attempt to develop a theory of local Moufang sets, which generalize Moufang…
We construct a Moufang loop $M$ of order $3^{19}$ and a pair $a,b$ of its elements such that the set of all elements of $M$ that associate with $a$ and $b$ does not form a subloop. This is also an example of a nonassociative Moufang loop…
In this paper the linear representations of analytic Moufang loops are investigated. We prove that every representation of semisimple analytic Moufang loop is completely reducible and find all nonassociative irreducible representations. We…
We develop a systematic framework for studying target space duality at the classical level. We show that target space duality between manifolds M and Mtilde arises because of the existence of a very special symplectic manifold. This…
The Noether currents generated by continuous Moufang tranformations are constructed and their equal-time commutators are found. The corresponding charge algebra turns out to be a birepresentation of the tangent Mal'ltsev algebra of an…