On infinite dimensional representations of *-algebras generated by five orthoprojections with a linear relation and an orthogonality relation

Abstract:
We investigate *-algebras generated by five orthoprojections $p_1,\ldots,p_5$ which satisfy a linear relation  $p_1+p_2+p_3+p_4+ap_5=be$ for some real numbers a and b, e is the identity element and an orthogonality relation $p_4p_5=0$. We find infinite dimensional irreducible representations of such algebras for special cases.