The construction of affine structures on virtually nilpotent groups.
Karel Dekimpe (1995)
Manuscripta mathematica
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Karel Dekimpe (1995)
Manuscripta mathematica
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Remm, E., Goze, Michel (2002)
International Journal of Mathematics and Mathematical Sciences
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Burde, Dietrich (1999)
Journal of Lie Theory
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Rafał Pikuła (2010)
Studia Mathematica
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Let G be a group generated by a set of affine unipotent transformations T: X → X of the form T(x) = A x + α, where A is a lower triangular unipotent matrix, α is a constant vector, and X is a finite-dimensional torus. We show that the enveloping semigroup E(X,G) of the dynamical system (X,G) is a nilpotent group and find upper and lower bounds on its nilpotency class. Also, we obtain a description of E(X,G) as a quotient space.
Bahturin, Yuri (2012)
Serdica Mathematical Journal
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2010 Mathematics Subject Classification: Primary 16W50, 17B70; Secondary 16R10. The main result is the classification, up to isomorphism, of all gradings by arbitrary abelian groups on the finitely generated algebras that are free in a nilpotent variety of algebras over an algebraically closed field of characteristic zero. The research was supported by an NSERC Discovery Grant #227060-09
Frederick M. Goodman, Holly Hauschild (2006)
Fundamenta Mathematicae
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The affine Birman-Wenzl-Murakami algebras can be defined algebraically, via generators and relations, or geometrically as algebras of tangles in the solid torus, modulo Kauffman skein relations. We prove that the two versions are isomorphic, and we show that these algebras are free over any ground ring, with a basis similar to a well known basis of the affine Hecke algebra.
D. Fried, W. Goldman, M.W. Hirsch (1981)
Commentarii mathematici Helvetici
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Cabezas, J.M., Gómez, J.R. (2001)
Journal of Lie Theory
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Lluis Puig (1988)
Inventiones mathematicae
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Ю.В. Хакимджанов (1989)
Algebra i Logika
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Lewis, Robert H., Moore, Guy D. (1997)
Experimental Mathematics
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Dietrich Burde (2006)
Open Mathematics
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In this survey article we discuss the origin, theory and applications of left-symmetric algebras (LSAs in short) in geometry in physics. Recently Connes, Kreimer and Kontsevich have introduced LSAs in mathematical physics (QFT and renormalization theory), where the name pre-Lie algebras is used quite often. Already Cayley wrote about such algebras more than hundred years ago. Indeed, LSAs arise in many different areas of mathematics and physics. We attempt to give a survey of the fields...
Jackson, Steven Glenn, Noël, Alfred G. (2006)
Experimental Mathematics
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Nicolas Spaltenstein (1982)
Mathematische Zeitschrift
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Rich, Michael (1973)
Portugaliae mathematica
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