Head of the research group

– prof.dr.sc. Dražen Adamović, PMF Zagreb, matematički odsjek

Group members

– Iva Ćuže, mag.edu.mat, FPMOZ Mostar

Department of Mathematics

Research areas:

  • Infinite dimensional Lie algebras
  • Representation theory
  • Vertex algebras
  • Fusion rules

Research description:

As a part of Croatian Science Foundation project 2634 Algebraic and combinatorial methods in vertex algebra theory and Center of Excellence QuantiXLie we study new methods in vertex algebra theory and theory of infinite dimensional Lie algebras. We study certain important classes of vertex algebras like W-algebras and their connection to logarithmic conformal field theory in physics. We use free field realization and screening operators in order to realize vertex algebras and their modules. We construct intertwining operators and calculate fusion rules in categories of modules over certain algebra of Virasoro type (Heisenberg-Virasoro and W(2,2) algebra). Furthermore, we study certain irrational C2-cofinite vertex algebras and their connection to the theory of quantum groups.

Plans for future research:

Continuation of ongoing research and its application to logarithmic conformal field theory. Focus on new results from area of physics and develop appropriate mathematical methods.

List of selected research papers:

  • Adamovic, D., Radobolja, G., (2016). On free field realizations of W(2,2)-modules. SIGMA, 12 (2016) 113, 13 pages.
  • Adamovic, D., Radobolja, G., (2015). Free fild realization of the twisted Heisenberg-Virasoro algebra at level zero and its applications. J. of Pure and Applied Algebra, 219 (10), 4322-4342.
  • Radobolja, G., (2013). Subsingular vectors in Verma modules, and tensor product of weight modules over the twisted Heisenberg-Virasoro algebra and W (2, 2) algebra. J. of Mathematical Physics 54 (7), 071701

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