Proskurin D. Wick *-algebras and their representations

Wick algebras and their representations are investigated in the dissertation. The necessary and sufficient condition for the existence of homogeneous Wick iideal is proved. Bozejko and Speicher theorem about positiviity of Fock inner product is improved. It is proved that for Wick algebras with braided operator of coeffiiciients the kernel of Fock representation is generated by largest quadratic ideal. A class of Wick algebras with non-braided operator of coefficients having the largest quadratic ideal is constructed. The irreducible representations of these algebras are described.