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. Misurati, Biproduct quasi-quantum groups of rank 2,
submitted.
7.
D. Bulacu, M. Misurati, Quasi-Hopf algebras of dimension 6,
submitted; arXiv
preprint arXiv:2410.03476.
8.
D. Bulacu, C. Menini,
M. Misurati, 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, Gheorghe-Ionuț
Șimon, 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,
On deformation theory of associative algebras 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