Ado's theorem

to get instant updates about 'Ado's Theorem' on your MyPage. Meet other similar minded people. Its Free!

X 

All Updates


Description:
In abstract algebra, Ado's theorem states that every finite-dimensional Lie algebra L over a field K of characteristic zero can be viewed as a Lie algebra of square matrices under the commutator bracket. More precisely, the theorem states that L has a linear representation ρ over K, on a finite-dimensional vector space V, that is a faithful representation, making L isomorphic to a subalgebra of the endomorphisms of V.

While for the Lie algebras associated to classical groups there is nothing new in this, the general case is a deeper result. Applied to the real Lie algebra of a Lie group G, it does not imply that G has a faithful linear representation (which is not true in general), but rather that G always has a linear representation that is a local isomorphism with a linear group. It was proved in 1935 by Igor Dmitrievich Ado of Kazan State University, a student of Nikolai Chebotaryov.

The restriction on the characteristic was removed later, by Iwasawa and Harish-Chandra.

References

  • I. D. Ado, Note on the representation of finite continuous groups by means of linear substitutions, Izv. Fiz.-Mat. Obsch. (Kazan') , 7 (1935) pp. 1–43 (Russian language)
  • translation in
  • Nathan Jacobson, Lie Algebras, pp. 202-203





Read More

No feeds found

All
Posting your question. Please wait!...


No updates available.
No messages found
Suggested Pages
Zid
Zid
Tell your friends >
about this page
 Create a new Page
for companies, colleges, celebrities or anything you like.Get updates on MyPage.
Create a new Page
 Find your friends
  Find friends on MyPage from