2019
Том 71
№ 4

# Roiter A. V.

Articles: 11
Article (Russian)

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

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

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

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)

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

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

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

Article (Ukrainian)

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

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

Brief Communications (Russian)

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

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

Article (Russian)

### $E$-systems of representations

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

Brief Communications (Russian)

### On the categary of representations

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

Article (Russian)

### Whole-number representations of a symmetrical group of third degree

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.