Talk:Semisimple representation

Wikipedia:Miscellany for deletion/Draft:Semisimple representation
Any editor nominating this for Deletion, I attempted to have this page deleted under MFD and the author of the page moved it to mainspace during the MFD. Per accepted convention I withdrew the MFD, however I would like to firmly register that I oppose any return to Draftspace without the stick of CSD:G13 being in place including a no REFUND allowed rule. Either the page survives in mainspace, it is returned to Draft namespace and it stays of the G13 rail, or it gets deleted without any allowance for WP:REFUND. Hasteur (talk) 01:09, 9 November 2019 (UTC)
 * No other editor suggested such a restriction on this page, and it cannot therefore be considered to have been imposed by consensus. I do not see any reason why this should be returned to draft status, but if it should be, it will be in precisely the same position as any other draft. The availability of refund is a general policy and cannot be foreclosed in advance by a singel editor, although an admin asked for a future REFUND on this page might consider this history. DES (talk)DESiegel Contribs 03:39, 9 November 2019 (UTC)

General definition of a semisimple rep
To respond to the edit summary “the more general semisimple objects don't really belong in the first sentence, ” by, first I don’t disagree. But it’s still important, I think, to mention semisimple module as well as semisimple operator are examples of semisimple representations in the lead; perhaps in the second paragraph. (Incidentally, the opposite is also possible in the sense: given a set of operators, one can consider the algebra generated by it and then a semisimple representation is also a semisimple module over that algebra.) I wonder what the best way is. —— Taku (talk) 21:13, 15 November 2019 (UTC)
 * Sure, at the very least we can create a section in the article body and then summarize that later in the lead. — MarkH21 (talk) 10:58, 16 November 2019 (UTC)
 * The thing is this article is about a specific type of a representation (as opposed to a representation in general) and so it seems strange to have a section that discusses the definition of a representation in a somehow generalized sense. Anyway, for now, I will add a few sentences to the "equivalent characterization" section; note the proof is abstract in that it doesn't care a representation is of a group, an algebra or a single operator. -- Taku (talk) 23:53, 17 November 2019 (UTC)
 * I think that having different sections for different kinds of representations is fine. For instance, adding to the existing sections on groups and Lie algebras. — MarkH21 (talk) 23:56, 17 November 2019 (UTC)
 * No, I am *against* such a structure. Because this article is about a rep not an algebraic object, the emphasis should be on the structure of a rep. For example, the article needs (and I am planning to add later) a discussion on multiplicity of simple reps; that's independent of whether one is considering a rep of a group or an algebra. (In fact, with due care, one can more ore less identify a rep of a Lie group and a rep of a Lie algebra.) -- Taku (talk) 01:02, 18 November 2019 (UTC)
 * Ah sorry, I misunderstood what you meant. But representations of algebras and operators are representations; should this just be about group representations? It wouldn’t be terrible to include a generalization section even if it was focused on group representations, particularly since “semisimple representation” may refer to them in literature (I also don’t mean to include semisimple objects in general). — MarkH21 (talk) 01:23, 18 November 2019 (UTC)
 * I am not sure if I follow. I am against structuring articles according to types of algebraic objects. In physics, *as far as I understand*, it's common to treat the same rep as a that of a Lie group and that of a Lie algebra. In other words, the focus is on a rep and you stay flexible about whether the action is through an algebra or a group. This is why it's a bad idea to have an article structure based on algebraic types (am I making sense?) -- Taku (talk) 22:56, 18 November 2019 (UTC)
 * I am for having a separate section on the infinite-dimensional rep case, since in that case, one usually has the *completion* of a semisimple representation, as opposed to a semisimple representation, as you have pointed out, (and so one needs an extra care). -- Taku (talk) 23:27, 18 November 2019 (UTC)
 * On the last point: another option is to have a section of a regular representation (which is semisimple rep or the completion of a semisimple rep in the interesting case). Maybe we don’t need to give a detailed discussion of an infinite-dimensional semisimple rep. —- Taku (talk) 03:25, 19 November 2019 (UTC)

Merge proposal
What is your justification for merging Isotypic component to this article? –LaundryPizza03 ( d c̄ ) 01:35, 11 July 2024 (UTC)


 * Thank you for asking. The rationale for the merger proposal is that the article isotypic component concerns about a particular instance of an isotypic component. This article also discusses an isotypic component but in a more general context and merging the former into this one should be helpful to the readers. —- Taku (talk) 05:09, 11 July 2024 (UTC)
 * I haven't taken my own look, but I guess that is okay. –LaundryPizza03 ( d c̄ ) 06:12, 11 July 2024 (UTC)