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SUMMARY:Svetlana Zhilina (Lomonosov Moscow State University\, Russia)
DTSTART:20231106T150000Z
DTEND:20231106T160000Z
DTSTAMP:20260423T035049Z
UID:ENAAS/47
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ENAAS/47/">O
 n the lengths of Okubo algebras</a>\nby Svetlana Zhilina (Lomonosov Moscow
  State University\, Russia) as part of European Non-Associative Algebra Se
 minar\n\n\nAbstract\nThe length function of a non-associative algebra desc
 ribes the guaranteed number of multiplications which will be sufficient to
  generate the whole algebra with its arbitrary generating set. In this tal
 k we present a new method for length computation based on the sequence of 
 differences between the dimensions of a certain sequence of subspaces. It 
 allows us to compute the length of an Okubo algebra A over an arbitrary fi
 eld. Namely\, if A contains either nonzero idempotents or zero divisors\, 
 then its length equals four\, and otherwise its length equals three. We al
 so show that\, in the latter case\, A is generated by any two elements whi
 ch do not belong to the same two-dimensional subalgebra. The talk is based
  on a joint work with Alexander Guterman.\n
LOCATION:https://researchseminars.org/talk/ENAAS/47/
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