# The Tits forms of tame algebras and their roots

### José Antonio Peña

Universidad Nacional Autónoma de México, México, D.F., Mexico### Andrzej Skowroński

Nicolaus Copernicus University, Torun, Poland

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## Abstract

We survey some old and recent results concerning properties of the Tits quadratic forms of triangular finite dimensional algebras of finite and tame representation type over an algebraically closed field, and realization of their roots as dimension vectors of indecomposable modules. In particular, we discuss when we may recover the representation type of a triangular algebra from the combinatorial properties of its Tits quadratic form.