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Ramji Lal

Publications and source records attributed to Ramji Lal.

4 recordsLinked to original sources
arXiv2026

Commutator identities, Lie product identities, and Multiplicative Lie algebras

The aim of this paper is to give a formal meaning of universal commutator identities and to see as to how the structure of multiplicative Lie algebra on a group is a potential candidate to describe universal commutator identities. We introduce some higher Schur multipliers. We shall also introduce and study Steinberg and Chevalley Multiplicative Lie algebras, the multiplicative Lie algebras with commutator identities among the root vectors describing Lie product relations. Free multiplicative Lie algebra on Steinberg and Chevalley groups are discussed.

math.GR↗
arXiv2023

Gyro-Groups, Gyro-splittings and Co-homology

In this paper, we study gyro-groups associated to groups, group extensions admitting gyro-sections, and corresponding co-homologies. We also describe the obstructions in terms of co-homomology. The notion of gyro-Schur Multiplier and that of gyro-Milnor $K_{2}$ group are introduced.

math.GR↗
arXiv2005

Transversals in non-discrete groups

The concept of `topological right transversal' is introduced to study right transversals in topological groups. Given any right quasigroup $S$ with a Tychonoff topology $T$, it is proved that there exists a Hausdorff topological group in which $S$ can be embedded algebraically and topologically as a right transversal of a subgroup (not necessarily closed). It is also proved that if a topological right transversal $(S, T_{S}, T^{S}, \circ)$ is such that $T_{S} = T^{S}$ is a locally compact Hausdorff topology on $S$, then $S$ can be embedded as a right transversal of a closed subgroup in a Hausdorff topological group which is universal in some sense.

math.GR↗