Quasi Quantum Groups and Monoidal Categories
Contract number 47/2022, Project CNCSIS
PN-III-P4_PCE-2021-0282
1. Daniel Bulacu (project leader)
2.
Sorin Dăscălescu
(experienced researcher)
3.
Maria Joița
(experienced researcher)
4.
Constantin
Năstăsescu (experienced researcher)
5.
Florin Panaite
(experienced researcher)
6. Dragoș Ștefan (experienced researcher)
7.
Anca Niță
(trainee researcher; project member until September 30, 2023)
8.
Moș Maria Magdalena (trainee researcher; project member
from November 2023)
Scientific
objectives
There
are three work-packages:
1.
New
classes of Frobenius-Lusztig kernels quasi quantum groups (qQGs for short)
2.
Quasi-quantum
groups of Nichols type and quasi-quantum shuffle groups
3.
Modular
categories defined by quasi-quantum groups and related structures.
The objectives corresponding to them
are:
Ø Construction of Uq(g) and
Frobenius-Lusztig kernels in the quasi-Hopf case.
Ø Generalization for L-R-crossed
products containing deformations with a 2-cocycle of a double biproduct as a
particular case.
Ø Determination of braided tensorial Hopf
algebras corresponding to certain qQG (quantum quasi-group) structures, as well
as certain factor algebras of these.
Ø Characterization of mixed qQGs in
categories of Hopf bimodules as quasi-Hopf algebras of biproduct type,
providing examples from abelian groups, universal Clifford algebras, and
(quasi-) universal quantum groups.
Ø Find necessary and sufficient
conditions for Yetter-Drinfeld modules over a qQG H to form a balanced and
ribbon category, respectively.
Ø Find the ribbon elements for a
quasi-quantum double group D(H) and interpretation of the obtained results in
terms of H.
Ø Study of possible connections between
finite (co)wreaths with associated monoidal/sovereign/braided/spherical/modular
(co)representation categories and certain properties of the Eilenberg-Moore
algebra defining the (co)wreath.
|
NR. CRT. |
BUDGET
ITEM |
2022 |
2023 |
2024 |
TOTAL |
|
1 |
PERSONEL
EXPENSES |
143.530 |
322.900 |
322.885 |
789.315 |
|
2 |
INDIRECT
EXPENSES |
25.674 |
63.492 |
61.485 |
150.651 |
|
3 |
TRAVEL
EXPENSES |
24.618 |
95.382 |
80.000 |
200.000 |
|
4 |
LOGISTIC
EXPENSES |
33.010 |
20.000 |
7.015 |
60.025 |
|
5 |
TOTAL |
226.832 |
501.774 |
471.385 |
1.199.991 |
Research
funded by this project
1.
C. Boboc, S. Dăscălescu,
L. van Wyk, Cyclic algebras, symbol algebras and gradings on matrices,
Linear Algebra and its Applications 688 (2024), 157-178.
2.
D. Bulacu, B.
Torrecillas, 1-cycle deformations for Yetter-Drinfeld
coalgebras, submitted.
3.
D. Bulacu, D.
Popescu, B. Torrecillas, Double wreath quasi-Hopf algebras, J. Algebra
622 (2025), 1-71.
4.
D. Bulacu, D.
Popescu, B. Torrecillas, Double biproduct quasi-quantum groups,
submitted.
5.
D. Bulacu, B.
Torrecillas, The quasi-Hopf analog of the Drinfeld-Jimbo quantum groups,
in preparation to be submitted.
6.
D. Bulacu, M.
Misuratti, Biproduct quasi-quantum groups of rank 2, submitted.
7.
D. Bulacu, M.
Misuratti, Quasi-Hopf algebras of dimension 6, submitted; arXiv
preprint arXiv:2410.03476.
8.
D. Bulacu, C. Menini,
M. Misuratti, Quasi-quantum groups obtained from Nichols algebras of
diagonal type, work in progress.
9.
S.
Dăscălescu, C. Năstăsescu, L. Năstăsescu: Graded
(quasi-) Frobenius rings, J. Algebra 620 (2023), 392-424.
10. S. Dăscălescu, C. Năstăsescu, L. Năstăsescu, Picard groups of quasi-Frobenius algebras and a question on Frobenius strongly graded algebras, accepted for publication in Publicacions Matemàtiques.
11.
F. Panaite, Two-sided
crossed products, submitted; arXiv preprint arXiv:2410.14908.
12.
F. Panaite, L-R
crossed products, submitted; arXiv preprint arXiv:2410.08429.
13.
M. Joiţa, Finsler
locally C*-modules, Bull. Malays. Math. Sci. Soc. 46 (2023), 86.
14.
M. Joiţa, The Shilov
boundary for a local operator system, submitted; arXiv preprint
arXiv:2409.10474.
15.
M. Joita, I.
Şimon, Injective envelopes for locally C*-algebras, submitted.
16.
L. Liu, A. Makhlouf,
C. Menini, F. Panaite, BiHom-NS-algebras, twisted Rota-Baxter operators and generalized
Nijenhuis operators, Results in Mathematics 78 (2023), article number: 251.
17.
A. Makhlouf, D. Ștefan,
Deformations of algebraic structures in monoidal categories, submitted.
18.
C. Ospel, F. Panaite, P. Vanhaecke,
Generalized NS-algebras, J. Pure Appl. Algebra 229 (2025), 107784.
Scientific
seminar
|
Tema |
Data |
Ora |
|
Reconstruction
theorems |
3.11.2022 |
12-14 |
|
Reconstruction
theorems |
10.11.2022 |
12-14 |
|
C*
algebras |
17.11.2022 |
12-14 |
|
C*
algebras |
24.11.2022 |
12-14 |
|
C*
algebras |
8.12.2022 |
12-14 |
|
C*
algebras |
15.12.2022 |
12-14 |
|
Frobenius
and separable algebras – classic version |
26.01.2023 |
12-14 |
|
Frobenius
and separable algebras – categorial version |
9.02.2023 |
12-14 |
|
Augmented
Frobenius algebras |
16.03.2023 |
12-14 |
|
Frobenius wreath algebras |
30.03.2023 |
12-14 |
|
Separable
wreath algebras |
13.04.2023 |
12-14 |
|
Morita
theory for wreath algebras |
27.04.2023 |
12-14 |
|
Nichols
algebras |
4.05.2023 |
12-14 |
|
Nichols
algebras |
18.05.2023 |
12-14 |
|
Nichols
algebras |
8.06.2023 |
12-14 |
|
Bimonadas and
Hopf monads |
19.10.2023 |
12-14 |
|
Structure
theorems for bimonads |
2.11.2023 |
12-14 |
|
Bimonads
defined by wreath algebras |
16.11.2023 |
12-14 |
|
Quasi-quantum
groups characterized by Hopf bimonads |
7.12.2023 |
12-14 |
|
Cohomology
of finite abelian groups |
26.01.2024 |
12-14 |
|
Spectral
sequences and their role in computing group cohomology classes |
7.02.2024 |
12-14 |
|
Projective
representations |
21.02.2024 |
12-14 |
|
Group
theoretical categories |
14.03.2024 |
12-14 |
|
Spherical
and fusion categories |
28.03.2024 |
12-14 |
|
Balanced and
ribbon categories |
11.04.2024 |
12-14 |
|
Deformation
theories for algebras |
7.05.2024 |
12-14 |
|
Cross
product algebras and biproducts |
14.05.2024 |
12-14 |
|
Duoidal
categories and bimonoids |
6.06.2024 |
12-14 |
|
Shuffle
quantum groups |
19.06.2024 |
12-14 |
|
Frobenius-Lusztig kernels |
9.10.2024 |
12-14 |
|
Free Hopf
algebras in non-strict monoidal categories |
24.10.2024 |
12-14 |
|
The Picard
group of a braided monoidal category |
12.11.2024 |
12-14 |
Scientific
and financial reports
2022
2023
2024