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Results tagged with reference-request
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user 85967
This tag is used if a reference is needed in a paper or textbook on a specific result.
18
votes
Hamiltonian, Lagrangian and Newton formalism of mechanics
The three formalisms of classical mechanics, i.e. the Newtonian, the Lagrangian (analytical mechanics) and the Hamiltonian (canonical formalism) are generally not equivalent to each other -at least no …
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10
votes
Up to date summary on semisimple Hopf algebra over $\mathbb{C}$
This is a question on an active area of research, with lots of work on it (for the general case of algebraically closed fields of char zero). It is historically and conceptually closely connected to K …
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9
votes
Supermanifolds — elementary introduction?
Some further references, that might be of interest for your purposes:
You can see at this article and the book Supermanifolds
Theory and Applications by Alice Rogers. The article discusses -among o …
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6
votes
Accepted
Representation of Heisenberg-Weyl elements and their exponentials
The Heisenberg-Weyl algebra or the Weyl algebra or the algebra of the Canonical Commutation Relations (CCR) is generated by the $p,q$ generators subject to the relation
$$
[q, p] = i \hbar I \ \ \ \ …
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5
votes
Accepted
The Ungraded Milnor-Moore Theorem
The "ungraded" version of the theorem -which is actually the version for the Hopf algebras- can be found in most of the classical references on the subject, although its statement and proof appears sc …
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5
votes
Accepted
Examples of particle systems with higher-order collisions
I understand that the OP's original focus is classical statistical mechanics. However, i think that the question is of interest from a more general viewpoint including the dynamical systems/integrabil …
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5
votes
Tannaka-Krein duality in Chari-Pressley's book
I do not know much about the Tannaka-Krein duality itself. But regarding the last part of your question
Also if somebody could cast some light on possible generalizations of this proposition (to the …
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5
votes
Accepted
Character formula for Lie superalgebras
I agree with the suggestion in the comments for searching the front of the math arXiv (as an entry point), because this is a quite broad and active topic (and i am not sure it can be fully covered wit …
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4
votes
Accepted
Typical and atypical modules for Lie superalgebras
Regarding the "what is happening in the super case"; yes i agree that in some sense, it has to do with the odd simple roots but i think it is deeper than that:
In the case of semisimple, complex, Lie …
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4
votes
Definition of subcoalgebra over a commutative ring
You are right.
In the case of an $R$-submodule $D$ of an $R$-coalgebra $C$, the correct definition for $D$ being a subcoalgebra of $C$ is your definition (2) and not the one posted in your notes. This …
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3
votes
Weyl's Branching Rule for $SU(N)$-Setting
Maybe the following paper might prove helpful to your question:
Masatoshi Yamazaki, Branching Diagram for Special Unitary Group SU(n), J. Phys. Soc. Jpn. 21, pp. 1829-1832 (1966)
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3
votes
Ideal structure of a tensor product of certain algebras
Well, i do not know the answer in general but since you are asking for a reference and if
there are some conditions on $A$ and $B$ that guarantee these are the only non-trivial ideals of $A \oti …
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3
votes
Hopf algebra kernels vs. algebra kernels
-too long for a comment-
I am a little confused about the way terminology is used in the OP.
Maybe i'm missing the point; in case i do not, the closest result i know of -quite general and does not ref …
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2
votes
Algebras Morita equivalent with the Weyl Algebra and its smash products with a finite group
I do not know much on recent developments related to the first three questions asked. However, i know of some old results related mainly to the fourth question:
If $A_1$ is the Weyl algebra over an al …
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2
votes
Practical example of Hamiltonian reduction
If i correctly understand your question, i think what you are talking about is the so called Poincare reduction method. This actually generalises Liouville integrability, in the sense that in the pres …
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