30 citations · 95 across the 24 of their papers we have counts for
16 papers · 1 filter
Growth in noncommutative algebras and entropy in derived categories
Dmitri Piontkovski
A noncommutative projective variety is defined, after Artin and Zhang, by a graded coherent algebra A, where the category of coherent sheaves is the quotient qgr(A) of the category…
Multilinear nilalgebras and the Jacobian theorem
Dmitri Piontkovski
If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states…
Bernstein algebras that are algebraic and the Kurosh problem
Dmitri Piontkovski, Fouad Zitan
We study the class of Bernstein algebras that are algebraic, in the sense that each element generates a finite-dimensional subalgebra. Every Bernstein algebra has a maximal algebra…
Entropy of monomial algebras and derived categories
Li Lu, Dmitri Piontkovski
Let A be a finitely presented associative monomial algebra. We study the category qgr(A) which is a quotient of the category of graded finitely presented A-modules by the finite-di…
Context-free languages and associative algebras with algebraic Hilbert series
Roberto La Scala, Dmitri Piontkovski
In this paper, homological methods together with the theory of formal languages of theoretical computer science are proved to be effective tools to determine the growth and the Hil…
Noncommutative algebras, context-free grammars and algebraic Hilbert series
Roberto La Scala, Dmitri Piontkovski, Sharwan K. Tiwari
In this paper we introduce a class of noncommutative (finitely generated) monomial algebras whose Hilbert series are algebraic functions. We use the concept of graded homology and…