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Finite Semisimple Loop Algebras of Indecomposable $RA$ Loops

  Published:2015-03-12
 Printed: Jun 2015
  • R. K. Sharma,
    Department Of Mathematics, Indian Institute of Technology Delhi, New Delhi, India
  • Swati Sidana,
    Department Of Mathematics, Indian Institute of Technology Delhi, New Delhi, India
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Abstract

There are at the most seven classes of finite indecomposable $RA$ loops upto isomorphism. In this paper, we completely characterize the structure of the unit loop of loop algebras of these seven classes of loops over finite fields of characteristic greater than $2$.
Keywords: unit loop, loop algebra, indecomposable $RA$ loops unit loop, loop algebra, indecomposable $RA$ loops
MSC Classifications: 20N05, 17D05 show english descriptions Loops, quasigroups [See also 05Bxx]
Alternative rings
20N05 - Loops, quasigroups [See also 05Bxx]
17D05 - Alternative rings
 

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