Malcev

Malcev is a Russian surname, transliterated from the Cyrillic Mal’cev and sometimes rendered Maltsev or Malcov. In mathematics, the name is most prominently associated with Anatoly Ivanovich Maltsev (1909–1967), a Soviet mathematician whose work spanned group theory, topology and Lie theory. Maltsev’s research helped shape several branches of algebra and its connections to geometry, and several concepts bear his name or the name’s variants.

Malcev algebras are a class of nonassociative algebras introduced by Maltsev in the study of Moufang loops. They generalize certain aspects of Lie algebras and play a role in the theory of nonassociative algebras and their applications in geometry and algebraic structures. The Malcev identity defines the structure and relates to the way elements interact under the nonassociative product.

Malcev completion, also known as the Malcev correspondence, refers to a construction that embeds a suitable discrete group into a simply connected nilpotent Lie group. In particular, finitely generated torsion-free nilpotent groups have a unique real (or rational) Malcev completion that preserves the group’s algebraic structure within a Lie group framework. This idea provides a bridge between discrete group theory and Lie theory and is used in the study of lattices, geometric group theory and algebraic topology.

Variants of the surname continue to appear in mathematical literature, with Maltsev and Mal’cev representing common transliterations. The Malcev lineage thus reflects a historical thread in the development of algebra, Lie theory and their geometric applications.