Quasi
Quantum Groups and Monoidal Categories
Contract number 47/2022, Project CNCSIS
PN-III-P4_PCE-2021-0282
Research
team
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:
-
The
structure of a qQG
with coalgebra projection
-
Construction
of Uq(g) and Frobenius-Lusztig kernels in the
quasi-Hopf case.
-
Generalization
for L-R-crossed products containing deformations with a 2-cocycle of a double
biproduct as a particular case.
-
Determination
of braided tensorial Hopf algebras corresponding to certain qQG
(quantum quasi-group) structures, as well as certain factor algebras of these.
-
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.
-
Find
necessary and sufficient conditions for Yetter-Drinfeld modules over a qQG H to form a balanced and ribbon category, respectively.
-
Find
the ribbon elements for a quasi-quantum double group D(H) and interpretation of
the obtained results in terms of H.
-
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.
D. Bulacu, B.
Torrecillas, 1-Homology for coalgebras in Yetter-Drinfeld categories, submitted.
2.
D. Bulacu, D. Popescu, B.
Torrecillas, Double wreath quasi-Hopf algebras, submitted.
3.
D. Bulacu, D. Popescu, B.
Torrecillas, Double biproduct quasi-quantum groups, submitted.
4.
D. Bulacu, B.
Torrecillas, The quasi-Hopf analog of the Drinfeld-Jimbo quantum groups,
work in progress.
5.
D. Bulacu, C. Menini, M. Misurati, Biproduct quasi-quantum groups of rank 2, work
in progress.
6.
D. Bulacu, C. Menini, M. Misurati, Quasi-quantum groups obtained from Nichols
algebras of diagonal type, work in progress.
7.
S. Dăscălescu,
C. Năstăsescu, L. Năstăsescu: Graded (quasi-)Frobenius
rings, J. Algebra 620 (2023), 392-424.
8.
S. Dăscălescu,
C. Năstăsescu, L. Năstăsescu, Picard groups of
quasi-Frobenius algebras and a question on Frobenius strongly graded algebras,
submitted.
9.
M. Joiţa, Finsler
locally C*-modules, Bull. Malays. Math. Sci. Soc. 46 (2023), 86.
10.
M. Joita, I. Simon, Injective
envelopes for locally C*-algebras, work in progress.
11.
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.
12.
A. Makhlouf, D.
Ștefan, Deformations of algebraic structures in monoidal categories,
work in progress.
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 |
Scientific
and financial reports
2022
2023