My research interests lie in the area of Groups, Rings, Lie and Hopf Algebras. The results obtained by me (often in cooperation with my colleagues) deal with the following matters:
- Identical relations and varieties of Lie and associative algebras and superalgebras,
- Enveloping algebras and representations of Lie algebras and superalgebras,
- Automorphism groups of certain Lie algebras,
- Structure and representations of locally finite Lie algebras,
- Algebras with actions and coactions of Hopf algebras,
- Graded algebras and applications.
I have written some monographs and textbooks (#3 below with my former students):
- Bahturin, J. A. Lectures on Lie algebras. Lectures given at Humboldt University, Berlin and Lomonosov University, Moscow. Studien zur Algebra und ihre Anwendungen [Studies in Algebra and its Applications], 4. Akademie-Verlag, Berlin, 1978. viii+126 pp.
- Bahturin, Yu. A. Identical relations in Lie algebras. Translated from the Russian by Bakhturin. VNU Science Press, b.v., Utrecht, 1987. x+309 pp. ISBN: 90-6764-052-2
- Bahturin, Yuri A.; Mikhalev, Alexander A.; Petrogradsky, Viktor M.; Zaicev, Mikhail V. Infinite-dimensional Lie superalgebras. de Gruyter Expositions in Mathematics, 7. Walter de Gruyter & Co., Berlin, 1992. x+250 pp. ISBN: 3-11-012974-4
- Bahturin, Yuri Basic structures of modern algebra. Mathematics and its Applications, 265. Kluwer Academic Publishers Group, Dordrecht, 1993. x+419 pp. ISBN: 0-7923-2459-5
The most recent published papers include:
- Bahturin, Yuri.; Strade, Helmut. Locally finite-dimensional simple Lie algebras. Mat. Sb. 185 (1994), no. 2, 3-32.
- Bahturin, Yuri.; Benkart, Georgia M.. Highest weight modules for locally finite Lie algebras. Modular interfaces...AMS/IP Studies in Math. 4 (1997), 1-31.
- Bahturin, Yuri.; Zaicev M. V. Identities of graded algebras. J. Algebra 205 (1998), no. 1, 1-12
- Bahturin, Yuri.; Linchenko, Vitaly. Identities of algebras with actions of Hopf algebras. J. Algebra, 202 (1998), 634 - 654.
- Bahturin, Yuri; Fischman, Davida; Montgomery, Susan. Bicharacters, twistings, and Scheunert's theorem for Hopf algebras. J. Algebra 236 (2001), no. 1, 246-276.
- Bahturin, Yu. A.; Sehgal, S. K.; Zaicev, M. V. Group gradings on associative algebras. J. Algebra, 241 (2001), 677-698.