Open AccessLie Algebras of Formal Power Series
Author(s) -
Min Ho Lee
Publication year - 2007
Publication title -
revista matemática complutense
Language(s) - English
Resource type - Journals
eISSN - 1696-8220
pISSN - 1139-1138
DOI - 10.5209/rev_rema.2007.v20.n2.16510
Subject(s) - formal power series , mathematics , noncommutative geometry , holomorphic function , pure mathematics , algebra over a field , laurent series , power series , series (stratigraphy) , holomorphic functional calculus , operator (biology) , formal group , finite rank operator , mathematical analysis , paleontology , biochemistry , chemistry , repressor , gene , transcription factor , banach space , biology
Pseudodifferential operators are formal Laurent series in the formal inverse -1 of the derivative operator whose coefficients are holomorphic functions. Given a pseudodifferential operator, the corresponding formal power series can be ob tained by using some constant multiples of its coefficients. The space of pseu dodifferential operators is a noncommutative algebra over C and therefore has a natural structure of a Lie algebra. We determine the corresponding Lie algebra structure on the space of formal power series and study some of its properties. We also discuss these results in connection with automorphic pseudodifferen tial operators, Jacobi-like forms, and modular forms for a discrete subgroup of SL(2, R)