A new simple Lie algebra of characteristic three

Author:
Marguerite Frank

Journal:
Proc. Amer. Math. Soc. **38** (1973), 43-46

MSC:
Primary 17B20

DOI:
https://doi.org/10.1090/S0002-9939-1973-0314924-0

MathSciNet review:
0314924

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Abstract: We define a restricted simple algebra of dimension 18 over an arbitrary field of characteristic 3. From a certain property of its Cartan decomposition, we show to be nonisomorphic to any known algebra of identical dimension.

**[1]**Gordon Brown,*Lie algebras of characteristic three with nondegenerate Killing form.*, Trans. Amer. Math. Soc.**137**(1969), 259–268. MR**0241485**, https://doi.org/10.1090/S0002-9947-1969-0241485-0**[2]**S. P. Demuškin,*Cartan subalgebras of the simple Lie 𝑝-algebras 𝑊_{𝑛} and 𝑆_{𝑛}*, Sibirsk. Mat. Ž.**11**(1970), 310–325 (Russian). MR**0262310****[3]**M. Frank,*On a theory relating matric Lie algebras of characteristic and subalgebras of the Witt-Jacobson algebra*, Progress Report I.T., Math. Dept., University of Minnesota, Minneapolis, Minn., 1943, pp. 107-121.**[4]**N. Jacobson,*Classes of restricted Lie algebras of characteristic 𝑝. II*, Duke Math. J.**10**(1943), 107–121. MR**0007749****[5]**Irving Kaplansky,*Lie algebras of characteristic 𝑝*, Trans. Amer. Math. Soc.**89**(1958), 149–183. MR**0099359**, https://doi.org/10.1090/S0002-9947-1958-0099359-7**[6]**A. I. Kostrikin,*A parametric family of simple Lie algebras*, Izv. Akad. Nauk SSSR Ser. Mat.**34**(1970), 744–756 (Russian). MR**0274539**

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DOI:
https://doi.org/10.1090/S0002-9939-1973-0314924-0

Article copyright:
© Copyright 1973
American Mathematical Society