Roiter A. V.
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.
Ukr. Mat. Zh. - 2002. - 54, № 6. - pp. 808-840
We consider numerical functions that characterize Dynkin schemes, Coxeter graphs, and tame 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.
Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1363-1396
A criterion of finite representability of dyadic sets is presented.
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.
Ukr. Mat. Zh. - 1995. - 47, № 11. - pp. 1451–1477
We prove that every finitely represented vectroid is determined, up to an isomorphism, by its completed biordered set. Elementary and multielementary representations of such vectroids (which play a central role for biinvolutive posets) are described.
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
Ukr. Mat. Zh. - 1967. - 19, № 2. - pp. 125–126
Ukr. Mat. Zh. - 1965. - 17, № 4. - pp. 124-129
Ukr. Mat. Zh. - 1965. - 17, № 2. - pp. 88-96
Ukr. Mat. Zh. - 1963. - 15, № 4. - pp. 448-453
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.