Bashkirov, Denis Aleksandrovich2015-02-242015-02-242014-11https://hdl.handle.net/11299/170096University of Minnesota Ph.D. dissertation. November 2014. Major: Mathematics. Advisor: Alexander A Voronov. 1 computer file (PDF); v, 54 pages.The present work concerns certain aspects of homotopy Lie and homotopy Batalin-Vilkovisky structures. In the first part we characterize a class of homotopy BV-algebras canonically associated to strongly homotopy Lie algebras and show that a category of strongly homotopy Lie algebras embeds into a certain subcategory of particularly simple homotopy Batalin-Vilkovisky algebras. In the second part of the work we introduce the notions of coboundary and triangular homotopy Lie bialgebras and discuss a possible a framework for quantization of such bialgebras.enMathematicsThesis or Dissertation