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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.
1
vote
Indecomposable representations of euclidean quivers
I am not particularly knowledgeable on the subject but I remember a recent workshop i attended where some lecturer referred to the book Finite Dimensional Algebras and Quantum Groups mentioning that i …
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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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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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2
votes
Hopf C-star algebra/comodules using a Fubini tensor product rather than the minimal tensor p...
Although i do not know much more to say, i recall i have seen this variant of the definition of the comodule you are describing, used in the context of Hopf-von Neumann algebras. See for example:
C …
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2
votes
Applications of number theory in dynamical systems
Some more references (which i think have not been mentioned in the other posts):
A couple of collections:
LMS 134: Number Theory & Dynamical Systems
Workshop on Combinatorics, Number Theory and Dynam …
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2
votes
Accepted
Is there Z_n graded supersymmetry?
The realizations (of an algebra through another algebra) you are speaking about are actually homomorphisms. And as such they should map between algebraic structures of the same kind: that is from alge …
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2
votes
Representation theory of $\text{SL}(2,\mathbb{Z})$
Far from being a specialist on the topic, section 4 of the article $\text{SL}_2(\mathbb{Z})$, by K. Conrad discusses non-congruence subgroups.
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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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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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1
vote
Commutative and Cocommutative Quantum Groups
If the definition of a finite quantum group, you use, is a pair $(A,\Phi)$ of a finite dimensional $C^*$-algebra $A$, with a comultiplication $\Phi$, such that $(A,\Phi)$ is a Hopf $*$-algebra, then t …
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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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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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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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1
vote
Reference request: numerical analysis of PDEs and integro partial differential equations
I am not a specialist on the subject, but having faced similar problems in the past, I know the situation can be quite tricky, especially since you put the question in general, including thus non-line …
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