On Homogeneous Standard Integral Table Algebras of Degree 4

ABSTRACT

In this paper we classify, up to exact isomorphism, the algebras in the title which contain a faithful element and in which every non-trivial table subset has dimension at least five.

Key Words:

• Group algebras
• Integral table algebras
• Schur rings
• Universal covering

Mathematics Subject Classification:

• Primary 13A99, 16W99, 20C05, 05E30

ACKNOWLEDGMENTS

The contribution of author Y. Erez to this article is a part of his Ph.D. thesis at Bar-Ilan University.

M. Muzychuk was partially supported by the Israeli Ministry of Absorption. The authors would like to thank the anonymous referee for valuable remarks and corrections.

Notes

¹We do not assume that A is finite dimensional.

²Here and later on, δ _ab is the Kronecker's delta.

³The elements y ₁, y ₂, y ₃ are not necessarily distinct.

Communicated by E. Zelmanov.