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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 14th 2012
   • (edited Oct 14th 2012)
   • PermaLink
   Author: Urs
   Format: Markdownthe entry _[[group algebra]]_ had been full of notation mismatch and also of typos. I have reworked it now.

   the entry group algebra had been full of notation mismatch and also of typos. I have reworked it now.

2. • CommentRowNumber2.
   • CommentAuthorTim_Porter
   • CommentTimeDec 7th 2013
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexI have added into [[group algebra]] a definition of the completed group algebra of a profinite group.

   I have added into group algebra a definition of the completed group algebra of a profinite group.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 19th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded statement and proof ([here](https://ncatlab.org/nlab/show/group+algebra#ComplexGroupAlgebraOfFiniteGroupAsDirectSumOfEndomorphismAlgebras)) that the complex group algebra of a finite group is isomorphic to the direct sum of linear endomrophism algebras of its complex irreps. <a href="https://ncatlab.org/nlab/revision/diff/group+algebra/21">diff</a>, <a href="https://ncatlab.org/nlab/revision/group+algebra/21">v21</a>, <a href="https://ncatlab.org/nlab/show/group+algebra">current</a>

   added statement and proof (here) that the complex group algebra of a finite group is isomorphic to the direct sum of linear endomrophism algebras of its complex irreps.

   diff, v21, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJul 9th 2023
   • (edited Jul 9th 2023)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to * [[Jacques Dixmier]], §13.2 in: *$C^\ast$-algebras*, North Holland (1977) for the case of locally compact topological groups <a href="https://ncatlab.org/nlab/revision/diff/group+algebra/24">diff</a>, <a href="https://ncatlab.org/nlab/revision/group+algebra/24">v24</a>, <a href="https://ncatlab.org/nlab/show/group+algebra">current</a>

   added pointer to

   • Jacques Dixmier, §13.2 in: $C^\ast$-algebras, North Holland (1977)

   for the case of locally compact topological groups

   diff, v24, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeDec 2nd 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * C. M. Edwards, [[John T. Lewis]], *Twisted group algebras I*, Communications in Mathematical Physics **13** (1969) 119–130 &lbrack;[doi:10.1007/BF01649871](https://doi.org/10.1007/BF01649871), [euclid:cmp/1103841535](https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-13/issue-2/Twisted-group-algebras-I/cmp/1103841535.full)&rbrack; * C. M. Edwards, [[John T. Lewis]], *Twisted group algebras II*, Communications in Mathematical Physics **13** (1969) 131–141 &lbrack;[doi:10.1007/BF01649872](https://doi.org/10.1007/BF01649872)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/group+algebra/30">diff</a>, <a href="https://ncatlab.org/nlab/revision/group+algebra/30">v30</a>, <a href="https://ncatlab.org/nlab/show/group+algebra">current</a>

   added pointer to:

   • C. M. Edwards, John T. Lewis, Twisted group algebras I, Communications in Mathematical Physics 13 (1969) 119–130 [doi:10.1007/BF01649871, euclid:cmp/1103841535]

   • C. M. Edwards, John T. Lewis, Twisted group algebras II, Communications in Mathematical Physics 13 (1969) 131–141 [doi:10.1007/BF01649872]

   diff, v30, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeDec 2nd 2023
   • (edited Dec 2nd 2023)
   • PermaLink
   Author: Urs
   Format: MarkdownItexmaybe this is the origin of the notion of group algebras: * [[Hermann Weyl]], §III.3 in: *Gruppentheorie und Quantenmechanik*, S. Hirzel, Leipzig (1931), translated by H. P. Robertson: *The Theory of Groups and Quantum Mechanics*, Dover (1950) &lbrack;[ISBN:0486602699](https://store.doverpublications.com/0486602699.html), [ark:/13960/t1kh1w36w](https://archive.org/details/ost-chemistry-quantumtheoryofa029235mbp/page/n15/mode/2up)&rbrack; ? <a href="https://ncatlab.org/nlab/revision/diff/group+algebra/30">diff</a>, <a href="https://ncatlab.org/nlab/revision/group+algebra/30">v30</a>, <a href="https://ncatlab.org/nlab/show/group+algebra">current</a>

   maybe this is the origin of the notion of group algebras:

   • Hermann Weyl, §III.3 in: Gruppentheorie und Quantenmechanik, S. Hirzel, Leipzig (1931), translated by H. P. Robertson: The Theory of Groups and Quantum Mechanics, Dover (1950) [ISBN:0486602699, ark:/13960/t1kh1w36w]

   ?

   diff, v30, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeDec 2nd 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded a (currently brief) paragraph ([here](https://ncatlab.org/nlab/show/group+algebra#OfCentralExtensionsAndTwistedGroupAlgebras)) on group algebras of central extensions relating to twisted group algebras <a href="https://ncatlab.org/nlab/revision/diff/group+algebra/30">diff</a>, <a href="https://ncatlab.org/nlab/revision/group+algebra/30">v30</a>, <a href="https://ncatlab.org/nlab/show/group+algebra">current</a>

   added a (currently brief) paragraph (here) on group algebras of central extensions relating to twisted group algebras

   diff, v30, current

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeDec 3rd 2023
   • (edited Dec 3rd 2023)
   • PermaLink
   Author: Urs
   Format: MarkdownItexhave spelled out ([here](https://ncatlab.org/nlab/show/group+algebra#ComplexGroupAlgebraOfCircleCentralExtension)) the case of complex group algebras of $\mathrm{U}(1)$-central extensions $G^\omega$ relating to $\omega$-twisted group algebras of $G$. <a href="https://ncatlab.org/nlab/revision/diff/group+algebra/31">diff</a>, <a href="https://ncatlab.org/nlab/revision/group+algebra/31">v31</a>, <a href="https://ncatlab.org/nlab/show/group+algebra">current</a>

   have spelled out (here) the case of complex group algebras of $\mathrm{U}(1)$-central extensions $G^\omega$ relating to $\omega$-twisted group algebras of $G$.

   diff, v31, current

9. • CommentRowNumber9.
   • CommentAuthorperezl.alonso
   • CommentTimeDec 3rd 2023
   • PermaLink
   Author: perezl.alonso
   Format: MarkdownItexjust a minor note, twisted group algebras are in general not Hopf algebras anymore

   just a minor note, twisted group algebras are in general not Hopf algebras anymore

10. • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeDec 4th 2023
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded pointer to: * [[Marc A. Rieffel]], *Lie Group Convolution Algebras as Deformation Quantizations of Linear Poisson Structures*, American Journal of Mathematics **112** 4 (1990) 657-685 &lbrack;[doi:10.2307/2374874](https://doi.org/10.2307/2374874), [jstor:2374874](https://www.jstor.org/stable/2374874)&rbrack; (here and at *[[strict deformation quantization]]*) <a href="https://ncatlab.org/nlab/revision/diff/group+algebra/32">diff</a>, <a href="https://ncatlab.org/nlab/revision/group+algebra/32">v32</a>, <a href="https://ncatlab.org/nlab/show/group+algebra">current</a>

    added pointer to:

    • Marc A. Rieffel, Lie Group Convolution Algebras as Deformation Quantizations of Linear Poisson Structures, American Journal of Mathematics 112 4 (1990) 657-685 [doi:10.2307/2374874, jstor:2374874]

    (here and at strict deformation quantization)

    diff, v32, current

11. • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeDec 4th 2023
    • PermaLink
    Author: Urs
    Format: MarkdownItexand pointer to * [[Nicolaas P. Landsman]], B. Ramazan, Ex. 11.1 in: *Quantization of Poisson algebras associated to Lie algebroids*, in: *Groupoids in Analysis, Geometry, and Physics*, Contemporary Mathematics **282** (2001) &lbrack;[arXiv:math-ph/0001005](https://arxiv.org/abs/math-ph/0001005), [ams:conm/282](http://www.ams.org/books/conm/282)&rbrack; (here and at *[[groupoid algebra]]*) <a href="https://ncatlab.org/nlab/revision/diff/group+algebra/34">diff</a>, <a href="https://ncatlab.org/nlab/revision/group+algebra/34">v34</a>, <a href="https://ncatlab.org/nlab/show/group+algebra">current</a>

    and pointer to

    • Nicolaas P. Landsman, B. Ramazan, Ex. 11.1 in: Quantization of Poisson algebras associated to Lie algebroids, in: Groupoids in Analysis, Geometry, and Physics, Contemporary Mathematics 282 (2001) [arXiv:math-ph/0001005, ams:conm/282]

    (here and at groupoid algebra)

    diff, v34, current

12. • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeDec 4th 2023
    • PermaLink
    Author: Urs
    Format: MarkdownItexalso pointer to: * [[Nicolaas P. Landsman]], Ex. 2 in: *Lie Groupoid $C^\ast$-Algebras and Weyl Quantization*, Communications in Mathematical Physics **206** (1999) 367–381 &lbrack;[doi:10.1007/s002200050709](https://doi.org/10.1007/s002200050709)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/group+algebra/34">diff</a>, <a href="https://ncatlab.org/nlab/revision/group+algebra/34">v34</a>, <a href="https://ncatlab.org/nlab/show/group+algebra">current</a>

    also pointer to:

    • Nicolaas P. Landsman, Ex. 2 in: Lie Groupoid $C^\ast$-Algebras and Weyl Quantization, Communications in Mathematical Physics 206 (1999) 367–381 [doi:10.1007/s002200050709]

    diff, v34, current