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The algebra of invariants of a complete path algebra

Samuel Quirino

Abstract

We prove that the algebra of invariants of a complete path algebra under the action of a homogeneous group of continuous algebra automorphisms is a complete path algebra and preserves finite or tame representation type.

The algebra of invariants of a complete path algebra

Abstract

We prove that the algebra of invariants of a complete path algebra under the action of a homogeneous group of continuous algebra automorphisms is a complete path algebra and preserves finite or tame representation type.

Paper Structure

This paper contains 4 sections, 10 theorems, 11 equations.

Table of Contents

  1. Introduction
  2. Invariants of a ring of non-commutative power series rings
  3. Invariants of a complete path algebra
  4. Invariants and representation types

Key Result

Proposition 2.2

Let $R$ be an algebra over a field $k$ with a filtration $\mu$ such that $R_0=k$. Then, R is the free associative (non-commutative) $k$-algebra on a set $X$ and $\mu$ is the formal degree induced from $\mu:X\to\mathbb{N}_{+}$ if and only if $R$ satisfies the weak algorithm.

Theorems & Definitions (20)

  • Remark 1.1
  • Remark 1.2
  • Definition 2.1
  • Proposition 2.2: Cohn
  • Theorem 2.3: Cohn
  • Definition 2.4
  • Proposition 2.5: Cohn
  • Corollary 2.6: Cohn
  • Theorem 2.7
  • proof
  • ...and 10 more