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The graded Cartan matrix and global dimension of 0-relations algebras

The graded Cartan matrix and global dimension of 0-relations algebras

The Cartan matrix C of a left artinian ring A , with indecomposable projectives P 1 ,…, P n and corresponding simples S i = P i / JP i , is an n × n integral matrix with entries C ij , the number of copies of the simple …