E7 (mathematics) | Wikipedia audio article
Channel: wikipedia tts
Date: 06/10/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/E7_(mathematics)


00:00:36 1 Real and complex forms
00:01:13 2 Esub7/sub as an algebraic group
00:01:50 3 Algebra
00:02:27 3.1 Dynkin diagram
00:02:45 3.2 Root system
00:03:04 3.2.1 An alternative description
00:03:41 3.3 Weyl group
00:04:18 3.4 Cartan matrix
00:05:50 4 Important subalgebras and representations
00:06:27 4.1 Esub7/sub Polynomial Invariants
00:07:22 5 Chevalley groups of type Esub7/sub
00:07:59 6 Importance in physics
00:09:12 7 See also
00:10:08 8 Notes
00:10:45 9 References
00:11:03 N
00:11:40 See also



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SUMMARY
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In mathematics, E7 is the name of several closely related Lie groups, linear algebraic groups or their Lie algebras e7, all of which have dimension 133; the same notation E7 is used for the corresponding root lattice, which has rank 7. The designation E7 comes from the Cartan–Killing classification of the complex simple Lie algebras, which fall into four infinite series labeled An, Bn, Cn, Dn, and five exceptional cases labeled E6, E7, E8, F4, and G2. The E7 algebra is thus one of the five exceptional cases.
The fundamental group of the (adjoint) complex form, compact real form, or any algebraic version of E7 is the cyclic group Z/2Z, and its outer automorphism group is the trivial group. The dimension of its fundamental representation is 56.