The structure of autodistributive algebras

The Structure of Galois Algebras

✍ George Szeto; Lianyong Xue 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 87 KB

Let B be a ring with 1 and G an automorphism group of B of order n for some integer n. It is shown that if B is a Galois algebra with Galois group G, then B is either a direct sum of central Galois algebras or a direct sum of central Galois algebras and a commutative Galois algebra. Moreover, when G

The structure of imprimitivity algebras

✍ Philip Green 📂 Article 📅 1980 🏛 Elsevier Science 🌐 English ⚖ 1009 KB

The Structure of the Partition Algebras

✍ Paul Martin 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 353 KB

Ä 4 1 1 2 2 3 3 4 4 5 5 Ž ÄÄ 4 as clusters, and of composition of partitions ab s Q. ␣ , ␣ , ␣ , ␣ , 1 2 3 4 Ä 4 Ä 4 Ä 4 4 . Ž ␣ , ␤ , ␤ , ␤ , ␤ , ␤ by an appropriate juxtaposition cf. p. 868 5 1 2 3 4 5 w x. of 2 . We define the elements of S , Ä␣ , ␤ 4 n Ä 4 Ä 4 Ä 4 Ä 4

The Lie Structure of Enveloping Algebras

✍ D.M. Riley; A. Shalev 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 551 KB

This paper examines the Lie structure of restricted universal enveloping algebras \(u(L)\) over fields of characteristic \(p>0\). It is determined precisely when \(u(L)\), considered as a Lie algebra, is soluble (for \(p>2\) ), nilpotent, or satisfies the Engel condition. 1993 Acadernic Press. Inc.

Structure matrices of algebras

✍ Michael P Drazin 📂 Article 📅 1984 🏛 Elsevier Science 🌐 English ⚖ 623 KB

On the Structure of Weak Hopf Algebras

✍ Dmitri Nikshych 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 252 KB

We study the group of group-like elements of a weak Hopf algebra and derive an analogue of Radford's formula for the fourth power of the antipode S; which implies that the antipode has a finite order modulo, a trivial automorphism. We find a sufficient condition in terms of TrðS 2 Þ for a weak Hopf