اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدInner ideals in Lie algebras and spherical buildings
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Arjeh M. Cohen
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The correspondence found by Faulkner between inner ideals of the Lie algebra of a simple algebraic group and shadows on long root groups of the building associated with the algebraic group is shown to hold in greater generality (in particular, over perfect fields of characteristic distinct from two).
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Let $min N$, $P(t)in C[t]$. Then we have the Riemann surfaces (commutative algebras) $R_m(P)=C[t^{pm1},u | u^m=P(t)]$ and $S_m(P)=C[t , u| u^m=P(t)].$ The Lie algebras $mathcal{R}_m(P)=Der(R_m(P))$ and $mathcal{S}_m(P)=Der(S_m(P))$ are called the $m$
-th superelliptic Lie algebras associated to $P(t)$. In this paper we determine the necessary and sufficient conditions for such Lie algebras to be simple, and determine their universal central extensions and their derivation algebras. We also study the isomorphism and automorphism problem for these Lie algebras.
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