4 Edinburgh Hodge Institute | ARTIN-53

The 53rd ARTIN meeting will be an Early Career Researchers meeting in Manchester. This means that PG students and postdocs in the ARTIN network are giving the talks — but all ARTIN members are encouraged to attend, to hear what's new! The meeting will start by 2pm on Thursday 26th April and end before 1pm on Friday 27th April.

This meeting is supported by the London Mathematical Society. It is being organized by Ibukun Ademehin.

Invited speakers:

• Miguel Couto (Glasgow),
• Francesca Fedele (Newcastle),
• Simon Crawford (Edinburgh),
• Angela Tabiri (Glasgow),
• Turki Mohammed (Sheffield).

Schedule of talks

• Miguel Couto (Glasgow) - Commutative-by-finite Hopf Algebras and their Finite Dual
26th April 2018, 2:00pm to 2:50pm Renold Building Room H1, University of Manchester. -- Show/hide abstract
Abstract:
The subject of this talk will be Hopf algebras and their dual theory. We will mostly focus on Hopf algebras which are "close" to being commutative. Some properties and examples of these Hopf algebras will be mentioned. Furthermore, we will see some results on their duals, some of its properties, decompositions and maybe some interesting Hopf subalgebras.
• Francesca Fedele (Newcastle) - A (d + 2)-Angulated Generalisation of a Theorem by Br¨uning
26th April 2018, 3:00pm to 3:50pm Renold Building Room H1, University of Manchester -- Show/hide abstract
Abstract:
Let d be a fixed positive integer, k an algebraically closed field and Φ a finite dimensional k-algebra with gldim Φ ≤ d. When d = 1, then mod Φ is hereditary and it follows from Br¨uning’s result [1, theorem 1.1] that there is a bijection between wide subcategories of mod Φ and wide subcategories of the bounded derived category D^b (mod Φ). For d ≥ 2, assume that there is a d-cluster tilting subcategory F  mod Φ and consider bar F := add{Σ^(id) F | i  Z} as a subcategory of D^b (mod Φ). The d-abelian category F plays the role of a higher mod Φ and the (d + 2)-angulated category bar F of its higher derived category. In this context, Br¨uning’s classic result generalises as follows.
Theorem: There is a bijection between functorially finite wide subcategories of F and functorially finite wide subcategories of bar F, sending a wide subcategory W of F to bar W.
For m and l positive integers such that (m − 1)/l = d/2, consider the C-algebra Φ = CA_m/(rad_{CA_m})^l from [2, section 4]. We use the above theorem to describe all the wide subcategories of bar F, where F is the unique d-cluster tilting subcategory of mod Φ.
References
[1] K. Br¨uning, Thick subcategories of the derived category of a hereditary algebra, Homology Homotopy Appl. 9 (2007), 165176.
[2] L. Vaso, n-cluster tilting subcategories of representation-directed algebras, preprint (2017). math.RT/ 1705.01031v1
• Break
26th April 2018, 4:00pm to 4:20pm Renold Building Room H1, University of Manchester
• Simon Crawford (Edinburgh) - Deformations of Quantum Kleinian Singularities Abstract:
26th April 2018, 4:20pm to 5:10pm Renold Building Room H1, University of Manchester. -- Show/hide abstract
Abstract:
In recent work, Chan--Kirkamn--Walton--Zhang defined a family of noncommutative rings which they call quantum Kleinian singularities, which may be thought of as noncommutative analogues of (the coordinate rings of) Kleinian singularities. Crawley-Boevey and Holland showed that one can deform Kleinian singularities, and in this talk I will show that the same is possible for quantum Kleinian singularities. I will discuss some of the properties of these deformations, and compare the behaviours of the deformations in the quantum and non-quantum cases. I will also define a family of algebras called deformed quantum preprojective algebras, and show that these are Morita equivalent to deformed quantum Kleinian singularities.
• Short talks
26th April 2018, 5:30pm to 6:00pm Renold Building Room H1, University of Manchester
• Break
27th April 2018, 12:00am to 12:15pm Renold Building Room H1, University of Manchester
• Angela Tabiri (Glasgow) - Reducible and Compact Real Form Singular Curves which are Quantum Homogeneous Spaces
27th April 2018, 10:00am to 10:50am Renold Building Room H1, University of Manchester -- Show/hide abstract
Abstract:
We construct a Hopf algebra $A(f,g)$ which contains the coordinate ring of a decomposable plane curve ( a curve of the form $f(y)=g(x)$) as a right coideal subalgebra and is free over the coordinate ring of the curve. For singular plane curves, examples of $A(f,g)$  enable us to show that a reducible curve (for example the coordinate crossing) and a curve with compact real form (for example the lemniscate) can be quantum homogeneous spaces. We show that the Gelfand-Kirillov dimension of  $A(f,g)$ depends on the degree of the plane curve and we give conditions for when these Hopf algebras are domains. Some well known algebras occur as special cases of the Hopf algebras constructed.
• Turki Mohammed (Sheffield) - Multiplication Modules
27th April 2018, 11:00am to 11:50am Renold Building Room H1, University of Manchester -- Show/hide abstract
Abstract:
The research is dedicated to studying a particular class of modules called multiplication modules. Let R be a ring. A left R -module M is called a multiplication module if for every submodule N of M, N=IM for some ideal I of R. If M is a left ideal of R then M is called a left multiplication ideal. A ring R is called a multiplication ring if every ideal of R is a left and right multiplication ideal. In this thesis, we give some properties and characteristics of multiplication modules over non-commutative ring. We deduced that if a multiplication R-module M is isomorphic to N^(I) ( a direct sum of I copies of R-module N) then card(I)=1. Also, we found out some criteria for a direct sum of R-modules to be a multiplication module. Additionally, we proved that a multiplication module has a unique indecomposable direct sum decomposition (if such decomposition exists). Moreover, we showed that the commutativity of product of a prime ideals of multiplication rings holds, and the commutativity of product of a prime ideal and an ideal not contained in it is satisfied as well. Also, we introduced the concept of epimorphic module, and we gave some properties of such class of modules. Over commutative rings, we gave some results inspired from cancellation law of multiplication modules, investigated when R-modules can be embedded in R and generalized some known results. Also, we introduced the concept of product of two submodules of a multiplication module and the notion of a divisor submodule. We introduced multiplication modules versions for primary decomposition theory and Chinese remainder theorem. Finally, we found out that if M is a finitely generated faithful multiplication R-module then the inclusions R  E  F are equalities where End_R (M) and F=End_E (M).
• Short talks
27th April 2018, 12:15pm to 12:45pm Renold Building Room H1, University of Manchester
(Open in Google Calendar)

Conference dinner
The conference dinner will be at Zouk restaurant by 7pm on the 26th.

Funds and accommodation
There are some additional funds to support participants from within the ARTIN network. If you plan to attend, please fill out the form here.

Participants are invited to make their own accommodation arrangements if they so require; funded participants can request reimbursement for this expense. The suggestions below are within 30 minutes travel time to the location of the meeting.

Birchfields Guest House,
Garden Hotel,
Stay Inn,
Ibis Manchester Portland Street,
Pendulum Hotel.
Alternatively, suitable accommodation can be searched for via a service such as booking.com.

Page last modified on Wednesday April 11, 2018 07:59:46 UTC