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math.RA2026
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…
math.RA2025
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…