For a quiver with potential (Q, W ) with an action of a finite cyclic group G, we study the skew group algebra ΛG of the Jacobian algebra Λ = P(Q, W ). By a result of Reiten and Riedtmann, the quiver Q G of a basic algebra η(ΛG)η Morita equivalent to ΛG is known. Under some assumptions on the action of G, we explicitly construct a potential W G on Q G such that η(ΛG)η ∼ = P(Q G , W G ). The original quiver with potential can then be recovered by the skew group algebra construction with a natural action of the dual group of G. If Λ is self-injective, then ΛG is as well, and we investigate this case. Motivated by Herschend and Iyama's characterisation of 2-representation finite algebras, we study how cuts on (Q, W ) behave with respect to our construction.2010 Mathematics Subject Classification. 16G20, 16S35.
Let G be a finite abelian group acting on a path algebra kQ by permuting the vertices and preserving the arrowspans. Let W be a potential on the quiver Q which is fixed by the action. We study the skew group dg algebra Γ Q,W G of the Ginzburg dg algebra of (Q, W ). It is known that Γ Q,W G is Morita equivalent to another Ginzburg dg algebra Γ Q G ,W G , whose quiver Q G was constructed by Demonet. In this article we give an explicit construction of the potential W G as a linear combination of cycles in Q G , and write the Morita equivalence explicitly. As a corollary, we obtain functors between the cluster categories corresponding to the two quivers with potentials.
For each prime number s we introduce examples of (s − 1)-and s-representation infinite algebras in the sense of Herschend, Iyama and Oppermann, which arise from skew group algebras of some metacyclic groups embedded in SL(s, C) and SL(s + 1, C). For this purpose, we give a description of the McKay quiver with a superpotential of such groups. Moreover we show that for s = 2 our examples correspond to the classical tame hereditary algebras of typeD.2010 Mathematics Subject Classification. 16G20; 16S35; 16E65.
The work presented in this paper shows how a single development evolved in a main Production Hub to unlock stranded resources, fast tracking subsequent marginal gas discoveries, by improving the flexibility of the subsea and treatment facilities. The approach was supported by a coherent activity about exploration program in the area, JV partnership and contracting strategy. During the Execution phase of a subsea development, a new discovery was made in deep water, 35 km from the Floating Production Unit (FPU). Following this discovery, given the potential for further developments in the area (stranded gas reservoirs and further new gas discoveries), the decision of considering the FPU as a future Production Hub has been taken and FPU has been converted accordingly. The inlet facilities have been designed to guarantee the possibility of receiving well fluids at different pressure levels (high pressure for the new developments and low pressure for productions in depletion) with high production flexibility. Several verifications have been performed to maximize the production flowrates at different pressure values, according to the envelope of data from exploration activities, via adequate arrangements for future expansion. These verifications considered the FPU as it is and with the implementation of minor and major modifications (including retrofitting offshore of new process modules). Design and timing of new equipment as minor/major brownfield modification have been set-up to cope with the modulate field profiles to keep FPU operating flowrate to its maximum value for longer time. In particular, the choice of new booster gas compressors has been planned, in order to select the best configuration for the most recent Hub development plan and to install them at the right time. Converting a barycentric infrastructure in a Hub ensures a significant reduction of CAPEX for future developments (limited to subsea tie-backs only), allowing to reconsider projects previously evaluated economically unsustainable. Moreover, the Hub shall guarantee a long-term gas production by continuous addition of new discoveries in the area, making it an essential facility for the energy future of the Country.
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