7 citations · 12 across the 8 of their papers we have counts for
8 papers
Algebra of formal vector fields on the line and Buchstaber's conjecture
Dmitri Millionschikov
Let L_1 denotes the Lie algebra of formal vector fields on the line which vanish at the origin together with their first derivatives. Buchstaber and Shokurov have shown that the un…
Adjoint cohomology of graded Lie algebras of maximal class
Dmitri Millionschikov
We compute explicitly the adjoint cohomology of two N-graded Lie algebras of maximal class (infinite dimensional filiform Lie algebras) m_0 and m_2. It is known that up to an isomo…
Massey products in graded Lie algebra cohomology
Dmitri V. Millionschikov
We discuss Massey products in a N-graded Lie algebra cohomology. One of the main examples is the positive part L_1 of the Witt algebra . We consider an associated graded algebra…
Multivalued functionals, one-forms and deformed de Rham complex
Dmitri V. Millionschikov
We discuss some applications of the Morse-Novikov theory to some problems in modern physics, where appears a non-exact closed 1-form (a multi-valued functional). We focus mainl…
Cohomology of graded Lie algebras of maximal class
Alice Fialowski, Dmitri V. Millionschikov
We compute the cohomology with trivial coefficients of two graded infinite-dimensional Lie algebras of maximal class, give explicit formulas for their representative cocycles. Also…
Deformations of graded Lie algebras and symplectic structures
Dmitri V. Millionschikov
We study symplectic structures on filiform Lie algebras -- nilpotent Lie algebras of the maximal length of the descending central sequence. In the present article we classify the L…