Speciality:
01.01.06 (Mathematical logic, algebra, and number theory)
Birth date:
5.01.1959
E-mail: ;
Keywords: associative algebras; finite groups; orthogonal decompositions; balanced systems of idempotents; group rings; combinatorial designs; finite geometries; translation planes; Hadamard matrices.
Subject:
The homogeneous algebras were classified. The following notions were introduced: 1) orthogonal decomposition (OD) of semisimple finite dimensional associative algebra; 2) balanced system of idempotents; 3) H-bijection of groups and H-isomorphism of group rings. The divisibility conjecture was confirmed in the case of commutative OD. The analogue of Wagner" Theorem for homogeneous ODs of type $nM_1$ of the matrix algebra $M_n(\mathbb C)$ was proved. The stable Abelian groups were classified, the rigidity and $\mathbb C$-basic rigidity of the family of subgroups which partition a group was obtained.
Main publications:
Ivanov D. N. H-biektsii grupp i H–izomorfizmy gruppovykh kolets // Matem. sbornik, 1997, 188(6), 27–46.
Ivanov D. N. Ortogonalnye razlozheniya assotsiativnykh algebr i sbalansirovannye sistemy idempotentov // Matem. sbornik, 1998, 189(12), 83–102.
Ivanov D. N. Sbalansirovannye sistemy iz primitivnykh idepotentov v algebrakh matrits // Matem. sbornik, 2000, 191(4), 67–90.
Ivanov D. N. O sbalansirovannykh sistemakh idempotentov // Matem. sbornik, 2001, 192(4), 73–86.
Ivanov D. N. Orthogonal decompositions and idempotent configurations in semisimple associative algebras // Comm. Algebra, 2001, 29(9), 3839–3887.
