论文标题
代数熵和有限图的路径代数的完整分类
Algebraic entropy and a complete classification of path algebras over finite graphs by growth
论文作者
论文摘要
Gelfand-Kirillov维度是一个良好的数量，用于对无限维代数的生长进行分类。在本文中，我们介绍了路径代数的代数熵。 For the path algebras, Leavitt path algebras and the path algebra of the extended (double) graph, we compare the Gelfand-Kirillov dimension and the entropy.我们通过维度，gelfand-kirillov维度和代数熵对有限图的路径代数进行完整分类。我们确实显示了这三个数量如何取决于图内的周期。此外，我们表明，代数熵在莫里塔对等上是保守的。另外，我们给出了路径代数和Leavitt路径代数中熵的几个例子。
The Gelfand-Kirillov dimension is a well established quantity to classify the growth of infinite dimensional algebras. In this article we introduce the algebraic entropy for path algebras. For the path algebras, Leavitt path algebras and the path algebra of the extended (double) graph, we compare the Gelfand-Kirillov dimension and the entropy. We give a complete classification of path algebras over finite graphs by dimension, Gelfand-Kirillov dimension and algebraic entropy. We show indeed how these three quantities are dependent on cycles inside the graph. Moreover we show that the algebraic entropy is conserved under Morita equivalence. In addition we give several examples of the entropy in path algebras and Leavitt path algebras.
