Current Questions

Understand tensors

- In what sense are tensors that which is invariant under change of frame?
- In what sense are there two kinds of such invariance: covariance and contravariance?
- Understand covariant derivative.
- Study Riemannian geometry, Gaussian curvature, metric tensor.
- Study Ricci tensor, general relativity.

Understand Hopf algebras

- What is a coalgebra?
- What is the antipode?

Understand real forms of Lie groups

- What is complexification? and in particular,
- complexification of a real Lie group?
- Chevalley complexification of a compact Lie group?
- the group of complex characters of the Hopf algebra of representative functions?

- How does it relate to the Cayley-Dickson construction?
- What are the rules for the Satake diagrams?
- Compact Lie groups

Understand the Lie group SU(2)

- Interpret the node of the Dynkin diagram.

Understand the Lie group SU(3)

- Interpret the link of the Dynkin diagram.

Understand the Lie group SU(N)

- Interpret the chain of the Dynkin diagram.

**Earlier questions**

- Peano axioms - do they presume a notion of "minimality" in defining the natural numbers?
- What do "globe", "globe category", "globular set" mean?
- Where in category theory do we find elementary symmetric functions?

Parsiųstas iš http://www.ms.lt/sodas/Book/MathQuestions

Puslapis paskutinį kartą pakeistas 2019 rugpjūčio 29 d., 23:06