3 papers
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…
math-ph2025
Degree of freedom count in linear gauge invariant PDE systems
Simon Lyakhovich, Dmitri Piontkovski
We consider not necessarily Lagrangian partial linear differential equations (PDE) with constant coefficients. Einstein proposed a definition of the"strength" of such a field theor…