Research
My research is in algebra, differential geometry, and their applications to theoretical physics. The main objects of my research include connections on fibre bundles, Lie groups and Lie algebras, their representations and generalizations. Particular attention is given to geometric methods in gauge field theories and to mathematical structures related to supersymmetry and supergeometry.
Keywords: differential geometry · connections · fibre bundles · Lie groups and Lie algebras · gauge field theories · supersymmetry · supergeometry
Current Research
Recently, my research has focused on algebraic structures with ternary multiplication and their possible applications to theoretical physics. Unlike the usual binary product, a ternary product is defined on three elements. I am interested in the algebraic and geometric properties of such structures and in their possible applications to physical models.
Keywords: ternary algebraic structures · 3-Lie algebras and superalgebras · transposed Poisson superalgebras · ternary Lie algebras at a cubic root of unity · ternary multiplication of 3-dimensional matrices · mathematical physics
Publications
Research papers and other scientific publications.
Research Projects
Information about research projects and collaborations will be placed here.