On C* algebras associated with L-canonical anti-comutation relations

Abstract:
We give a description of irreducible representations of commutation relations of the following forms: $a^*(i)a(i)+a(i)a^*(i)=1$, $a^*(i)a(j)=l(i,j)a(j)a^*(i)$, $i<j$,
$a(j)a(i)-l(i,j)a(i)a(j)$, $i<j$, $(l(i,j))^n=1$. The corresponding enveloping $C^*$ algebras are described.