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.
Biography
Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1981 (department of higher algebra). Ph.D. was defended in 1990. I belong to the school of A. I. Kostrikin.
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.
D. N. Ivanov, “Degrees of Irreducible Characters and Dimensions of Hadamard Algebras”, Mat. Zametki, 98:2 (2015), 230–236; Math. Notes, 98:2 (2015), 258–264
D. N. Ivanov, “Orthogonal decompositions of direct sums and tensor products of algebras”, Uspekhi Mat. Nauk, 64:2(386) (2009), 205–206; Russian Math. Surveys, 64:2 (2009), 393–395
2007
8.
D. N. Ivanov, “Homogeneous commutative orthogonal decompositions of semisimple algebras”, Uspekhi Mat. Nauk, 62:6(378) (2007), 173–174; Russian Math. Surveys, 62:6 (2007), 1204–1206
D. N. Ivanov, “On balanced bases”, Mat. Zametki, 77:2 (2005), 213–218; Math. Notes, 77:2 (2005), 194–198
10.
D. N. Ivanov, “The dimension of a Hadamard algebra is divisible by 4”, Uspekhi Mat. Nauk, 60:2(362) (2005), 163–164; Russian Math. Surveys, 60:2 (2005), 357–358
D. N. Ivanov, “An analogue of Wagner's theorem for decompositions of matrix algebras”, Mat. Sb., 195:11 (2004), 13–30; Sb. Math., 195:11 (2004), 1557–1574
2003
13.
D. N. Ivanov, “Hadamard decompositions of semisimple associative algebras”, Uspekhi Mat. Nauk, 58:4(352) (2003), 147–148; Russian Math. Surveys, 58:4 (2003), 789–790
D. N. Ivanov, “Selected topics of the theory of orthogonal decomposition of associative algebras”, Fundam. Prikl. Mat., 4:1 (1998), 187–197
17.
D. N. Ivanov, “Orthogonal decompositions of associative algebras, and balanced systems of idempotents”, Mat. Sb., 189:12 (1998), 83–102; Sb. Math., 189:12 (1998), 1819–1838
D. N. Ivanov, “$\mathscr H$-bijections of groups and $\mathscr H_R$-isomorphisms of group rings”, Mat. Sb., 188:6 (1997), 27–46; Sb. Math., 188:6 (1997), 823–841
D. N. Ivanov, “Automorphisms of orthogonal decompositions and of group algebras of groups with partitions”, Mat. Sb., 186:9 (1995), 77–86; Sb. Math., 186:9 (1995), 1303–1312
D. N. Ivanov, “An analogue of a theorem of Wagner for orthogonal decompositions of the matrix algebra
$M_n(\mathbb C)$”, Uspekhi Mat. Nauk, 49:1(295) (1994), 215–216; Russian Math. Surveys, 49:1 (1994), 237–238
D. N. Ivanov, “A theorem on the subalgebras forming an orthogonal
decomposition of an associative algebra”, Uspekhi Mat. Nauk, 44:2(266) (1989), 231–232; Russian Math. Surveys, 44:2 (1989), 283–284
D. N. Ivanov, “Orthogonal decompositions of Lie algebras of the type $A_{p^n-1}$ and $D_n$ with a finite number of classes of similar invariant sublattices”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1989, no. 2, 40–43
D. N. Ivanov, “Orthogonal decompositions of Lie algebras of type $ A_{p^n-1}$ and isotropic fiberings”, Uspekhi Mat. Nauk, 42:4(256) (1987), 187–188; Russian Math. Surveys, 42:4 (1987), 141–142
