On a group that acts freely on an Abelian group.
On Balancing and Lucas-balancing Quaternions
The aim of this article is to investigate two new classes of quaternions, namely, balancing and Lucas-balancing quaternions that are based on balancing and Lucas-balancing numbers, respectively. Further, some identities including Binet's formulas, summation formulas, Catalan's identity, etc. concerning these quaternions are also established.
On classical invariant theory and binary cubics
Let be a reductive complex algebraic group, and let denote the algebra of invariant polynomial functions on the direct sum of copies of the representations space of . There is a smallest integer such that generators and relations of can be obtained from those of by polarization and restitution for all . We bound and the degrees of generators and relations of , extending results of Vust. We apply our techniques to compute the invariant theory of binary cubics.
On Cycles in Flag Manifolds.
On Dye's condition in nilpotent groups of class 2
On Faithful Representations of the Holomorph of Lie Groups.
On K2 (...) and presentations of SLn (...) in the real quadratic case.
On maximal compact subsemigroups of the endomorphism semigroup of an n-dimensional complex vector space.
On observable subgroups of complex analytic groups and algebraic structures on analytic homogeneous spaces.
On the character variety of group representations in SL (2, C) and PSL (2, C).
On the exponential map of almost simple real algebraic groups.
On the exponential map of the Lie groups locally isomorphic to .
On the Generation of Dyadic Integral Orthogonal Groups.
Orbits of the Weyl group and a theorem of DeConcini and Procesi