The mappings of degree 1
The maps of the form f(x)=∑i=1nai⋅x⋅bi, called 1-degree maps, are introduced and investigated. For noncommutative algebras and modules over them 1-degree maps give an analogy of linear maps and differentials. Under some conditions on the algebra 𝒜, contractibility of the group of 1-degree isomorphis...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA/2006/90837 |
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| Summary: | The maps of the form f(x)=∑i=1nai⋅x⋅bi,
called 1-degree maps, are introduced and investigated. For
noncommutative algebras and modules over them 1-degree maps give
an analogy of linear maps and differentials. Under some conditions
on the algebra 𝒜, contractibility of the group of
1-degree isomorphisms is proved for the module l2(𝒜).
It is shown that these conditions are fulfilled for the algebra of
linear maps of a finite-dimensional linear space. The notion of
1-degree map gives a possibility to define a nonlinear Fredholm
map of l2(𝒜) and a Fredholm manifold modelled by
l2(𝒜). 1-degree maps are also applied to some
problems of Markov chains. |
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| ISSN: | 1085-3375 1687-0409 |