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Abelian Hessian algebra and commutative Frobenius algebra

✍ Scribed by Yuncherl Choi; Hyuk Kim; Kyunghee Kim

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 254 KB
Volume: 428
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2007.11.020

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✦ Synopsis

In this paper we study the structure of an abelian Hessian algebra. First we show that it can be decomposed into unital abelian Hessian algebras and a complete abelian Hessian algebra (abbreviated by CAHA). Then we show that a unital one is in fact a hyperbolic extension of a CAHA. Next we investigate the structure of CAHA by studying double filtration obtained canonically from lower and upper annihilator series. This double filtration together with j-invariant of ternary cubic form give a complete classification of CAHA up to dimension 6.

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