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SUMMARY:Jari Desmet (Ghent University\, Belgium)
DTSTART:20250407T150000Z
DTEND:20250407T160000Z
DTSTAMP:20260423T035739Z
UID:ENAAS/117
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ENAAS/117/">
 Jordan algebras and automorphism groups of Matsuo algebras</a>\nby Jari De
 smet (Ghent University\, Belgium) as part of European Non-Associative Alge
 bra Seminar\n\n\nAbstract\nPrimitive axial algebras of Jordan type half we
 re introduced by Jonathan Hall\, Felix Rehren and Sergey Shpectorov in 201
 5\, generalizing Jordan algebras by requiring that their idempotents satsi
 fy the Peirce decomposition. More specifically\, primitive axial algebras 
 of Jordan type $\\frac{1}{2}$ are commutative non-associative algebras gen
 erated by idempotents $a$ such that their multiplication operators $L_a$ a
 re diagonalizable with eigenvalues $\\{1\,0\,\\frac{1}{2}\\}$\, such that 
 the fusion laws $V_1 = \\langle a\\rangle$\, $V_0^2 \\subseteq V_0$\, $V_0
 V_{\\frac{1}{2}} \\subseteq V_{\\frac{1}{2}}$ and $V_{\\frac{1}{2}}^2 \\su
 bseteq V_0 \\oplus V_1$ hold\, where $V_\\lambda$ is the $\\lambda$-eigens
 pace of $L_a$. The most well-known examples of this class of algebras are 
 either Jordan algebras or Matsuo algebras\, certain non-assocative algebra
 s related to 3-transposition groups that Atsushi Matsuo discovered while s
 tudyin vertex operator algebras. In this talk\, we will sketch how one can
  distinguish these two classes in terms of their automorphism groups. In p
 articular\, primitive axial algebras of Jordan type half with large automo
 rphism groups are automatically Jordan while the automorphism groups of no
 n-Jordan Matsuo algebras are usually finite\, with one infinite family of 
 exceptions.\n
LOCATION:https://researchseminars.org/talk/ENAAS/117/
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