2019
Том 71
№ 4

All Issues

Roiter A. V.

Articles: 11
Article (Russian)

Singular locally scalar representations of quivers in Hilbert spaces and separating functions

Redchuk I. K., Roiter A. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 6. - pp. 796–809

We consider locally scalar representations of extended Dynkin graphs in Hilbert spaces. The relation between these representations and the function ρ( n ) = 1 + ( n − 1 ) / ( n + 1 ) is established. We construct a family of separating functions that generalize the function ρ and play a similar role in a broader class of graphs.

Article (Russian)

The Norm of a Relation, Separating Functions, and Representations of Marked Quivers

Nazarova L. A., Roiter A. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 6. - pp. 808-840

We consider numerical functions that characterize Dynkin schemes, Coxeter graphs, and tame marked quivers.

Brief Communications (Russian)

Finitely Represented $K$-Marked Quivers

Belousov K. I., Nazarova L. A., Roiter A. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 4. - pp. 550-555

We present necessary and sufficient conditions for the finite representability of K-marked quivers.

Article (Russian)

Finitely representable dyadic sets

Nazarova L. A., Roiter A. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1363-1396

A criterion of finite representability of dyadic sets is presented.

Article (English)

Finitely represented dyadic sets and their multielementary representations

Belousov K. I., Nazarova L. A., Roiter A. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 11. - pp. 1465–1477

We obtain the direct reduction of representations of a dyadic set S such that |Ind C(S)| < ∞ to the bipartite case.

Article (Ukrainian)

Representations of finite p-groups over the ring of formal power series with integral p-adic coefficients

Gudivok P. M., Oros V. M., Roiter A. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1992. - 44, № 6. - pp. 753–765

Article (Ukrainian)

Integral p-adic representations and representations over a ring of residue classes

Nazarova L. A., Roiter A. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1967. - 19, № 2. - pp. 125–126

Brief Communications (Russian)

Divisibility in the category of representations over a complete local Dedekind ring

Roiter A. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1965. - 17, № 4. - pp. 124-129

Article (Russian)

$E$-systems of representations

Roiter A. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1965. - 17, № 2. - pp. 88-96

Brief Communications (Russian)

On the categary of representations

Roiter A. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1963. - 15, № 4. - pp. 448-453

Article (Russian)

Whole-number representations of a symmetrical group of third degree

Nazarova L. A., Roiter A. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1962. - 14, № 3. - pp. 271-288

The authors discuss whole-number representations to a symmetrica! group of the third degree. It is shown that there exists only a finite number, i. e. ten, prime representations of this group. The dimensions of the prime representations do not exceed the order of the group.
It is further shown that the factoring of any representation into a direct sum of primes is univalent.
Thus the first example has been given of a complete description of whole-number representations of a non-commutative group.