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Polynomial and Polygonal Connections between Idempotents in Finite‐Dimensional Real Algebras
Author(s) -
Esterle J.,
Giol J.
Publication year - 2004
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303002820
Subject(s) - mathematics , path (computing) , polynomial , mathematics subject classification , degree (music) , combinatorics , set (abstract data type) , component (thermodynamics) , lie algebra , pure mathematics , discrete mathematics , algebra over a field , mathematical analysis , computer science , physics , acoustics , thermodynamics , programming language
Let P (A) be the set of idempotents in a finite‐dimensional real algebra A . Let p and q be idempotents that lie in the same component of P (A) . Then, among the continuous paths connecting p and q in P (A) , there exist a polynomial path of degree at most 3 and a polygonal path consisting of at most three segments. 2000 Mathematics Subject Classification 46H10, 16P10.