Theory of linear G-difference equations
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https://hdl.handle.net/10037/2058Date
1997-12-17Type
Journal articleTidsskriftartikkel
Peer reviewed
Abstract
We introduce the notion of difference equation defined on a structured
set. The symmetry group of the structure determines the set of difference
operators. All main notions in the theory of difference equations are
introduced as invariants of the action of the symmetry group. Linear equations
are modules over the skew group algebra, solutions are morphisms relating a
given equation to other equations, symmetries of an equation are module endomorphisms
and conserved structures are invariants in the tensor algebra of
the given equation.
We show that the equations and their solutions can be described through
representations of the isotropy group of the symmetry group of the underlying
set. We relate our notion of difference equation and solutions to systems of
classical difference equations and their solutions and show that out notions
incluse these as a special case.
Description
This is the author’s final accepted manuscript
Publisher
SpringerCitation
Acta Applicandae MathematicaeMetadata
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